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Selling Put Options: How to Get Paid for Being Patient
You don’t have to let the market dictate what price you’ll pay for an awesome company. You can name your own price instead, and get paid to wait for the stock to dip to that level.
That’s what selling put options allows you to do.
When you sell a put option on a stock, you’re selling someone the right, but not the obligation, to make you buy 100 shares of a company at a certain price (called the “strike price”) before a certain date (called the “expiration date”) from them.
They’re paying you for this option to increase their own flexibility, and you’re getting paid to decrease your flexibility.
But by doing this in a smart way, you can get paid to do something you already wanted to do anyway buy shares of a great company if they dip in price. Then you can hold them for as long or short of a time as you want to.
By selling put options, you can:
 Generate doubledigit income and returns even in a flat, bearish, or overvalued market. You don’t need a strong bull market or fast business growth for great investment returns.
 Give your portfolio 10% or so downside protection in the event of a market crash. In other words, if the market drops 25%, your equity positions would likely only drop 15%.
 Enter stock positions at exactly the price you want, and keep your cost basis low. Buy during dips and get a better value than the current market price offers.
Like any tool, there’s an appropriate time and place to sell put options, and other times where it’s not an ideal tactic.
When used correctly, this is a sophisticated and underused way of entering equity positions, and this article provides a detailed overview with examples on how to do it.
Putselling example
Suppose you want to buy shares of a toptier railroad company with a strong balance sheet.
Over the last twelve months, it has made $1.80 in earnings per share, and currently trades at $30.50 per share. It pays 50% of its earnings in dividends, over the last ten years has grown earnings by an average of 7% per year with moderate volatility, and there’s no clear catalyst ahead that you expect to significantly change these growth rates. This gives it a P/E ratio of 16.9 and a PEG ratio of 2.4.
First, you need to determine what the fair value of the stock is, using discounted cash flow analysis or a similar valuation technique.
Using the fair value calculator that comes with OptionWeaver, this stock has a fair value of $33.33.

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Suppose that after deeper analysis, you decide the business is solid, and that you’d love to pick up shares at a 10% discount to fair value, which would mean under about $30.
That would give you a margin of safety in case the company grows slightly slower than expected, and would improve your overall returns if your growth estimates are accurate.
You could just… sit around and wait and watch, and maybe it’ll come down to $30 or below after a mediocre quarterly earnings release, and you’ll buy it then. Or maybe it won’t come down that low anytime soon, or ever. And for every month that it doesn’t, your cash is sitting on the sidelines and not earning any real returns.
A second method is simply to invest elsewhere. Maybe there’s another railroad trading at a better value that you can invest in instead. Or maybe you found a pipeline company that looks like a great investment at current prices. But what if the whole market is overvalued, and you’re having trouble finding anything trading at a discount to fair value?
The smart method here is to sell one or more cashsecured put options to take on the obligation to potentially buy the shares at a certain price before a certain date, and get paid money up front for taking on that obligation. You obligate yourself to do what you wanted to do anyway buy the stock if it dips.
The investor that buys the option from you now has the choice, but not the obligation, to decide to sell you the shares at the strike price on or before the expiration date. As the seller, you have the obligation to buy them at the strike price if she decides to exercise the option to sell them to you.
To see current option prices, you just look up an option table, such as on Google Finance or Yahoo Finance or through your online broker. In this example, I’m looking at the put table for an expiration date 3.5 months in the future, and the current share price is $30.50:
Put Table: 3.5 months until expiration
Click here for a bigger version of the image.
Strike: This is the strike price that you would be obligated to buy the shares at if the option buyer chooses to exercise their option to assign them to you.
Price: This is the price that the option has been selling for recently. This is basically how much the option buyer pays the option seller for the option.
Change: This shows you the recent changes in the option pricing.
Bid: This is approximately what you’ll receive in option premiums per share up front if you sell the put. A market maker agrees to pay you this amount to buy the option from you.
Ask: This is what an option buyer will pay the market maker to get that option from him. The difference between “bid” and “ask” is the market maker’s profit. He’s the middle man between option buyers and sellers that makes this a liquid market.
Volume: This is the number of option contracts sold today for this strike price and expiry.
Open Interest: This is the number of existing options for this strike price and expiration. It’s the sum of all option volume leading up to today, minus any option positions that were closed prematurely.
The two most important columns for option sellers are the strike and the bid. The strike is the amount you’re agreeing to buy the shares for if the option is exercised, and the bid is roughly the amount of premium you can expect to earn when you sell the option.
As you can see in the picture, there are all sorts of options at different strike prices that pay different amounts of premiums. And this picture only shows one expiration date there are other pages for other dates.
In this example, the option that stands out to me as a good choice is the one with a strike price of $30. It’s just below the current stock price of $30.50 and offers a decent premium bid price of $1.43.
Let’s go with this one:
Click here for a bigger image.
If you sell this option, it means you’ll receive $143 now from the option buyer, and you’ll be obligated to buy 100 shares of this railroad company at $30 each if the buyer wants, for a total of $3,000, any time before the expiration date of the option in 3.5 months.
If you sell several options, you’ll be obligated to buy several hundred shares. Each option is for 100 shares.
A conservative investor always has cash available to back this up. You would have $3,000 in cash for each of these options in your brokerage account locked away and ready to buy the shares if they are assigned. This makes it cashsecured. If you do not have the cash available, it would be called a “naked” put, which is highly speculative and not what this guide covers.
In this case, you really need just $2,857 in cash up front, because as soon as you sell the option, you’ll receive the $143 in premiums right away which will bring you up to the full $3,000 amount needed for it to be cashsecured.
So, let’s say you sell this option. Here are your inputs, as well as the potential outputs of what can occur, courtesy of OptionWeaver:
Let’s go over those possible outcomes.
Possibility A: The stock stays over $30 at expiration
If, over the next 3.5 months, the railroad generally stays above $30/share, the option buyer will likely not assign you the shares, since there would be no reason for her to force you to pay exactly $30/share when the market price is already over $30/share. Her option will expire worthless, you’ll keep your $143 premium, and your $3,000 in secured cash will be freed up for selling another option.
Here’s the rate of return calculation if the option expires:
$143 / $2,857 = 0.05 = 5%
You made a 5% rate of return on your initial cash in about 3.5 months. This would be about 18% annualized returns on your money if you do this a few more times for the rest of the year. Compare this to the historical S&P 500 return of around 9%. You’re getting paid a hefty sum of money compared to historical equity returns to just sit around and wait for a price dip for a company you want to own.
Possibility B: The stock declines under $30 at expiration
Let’s say that in 3.5 months, when this option is about to expire, the railroad stock is selling for $29.50/share. So, it dipped a bit. You still get to keep the $143 premium, and the option buyer will assign you to buy the 100 shares for $30 each.
This means that your effective cost basis for the purchase of these shares was only $28.57, which is below your target buy price, like you wanted. You ended up having to buy them for $30 each, but you also received a $1.43/share premium up front, offsetting part of the cost. The net cost basis is that you had to pay $28.57/share, or $2,857 for 100 shares.
And now, you currently own 100 shares of a fine railroad company that currently trade for $29.50 each. You bought a great company at a great price, and now hopefully you can expect plenty of capital appreciation and dividends over time.
Put option risk profile
Selling put options at a strike price that is below the current market value of the shares is a moderately more conservative strategy than buying shares of stock normally. Your downside risk is moderately reduced for two reasons:
 Your committed buy price is below the current market price
 You receive an option premium up front, regardless of what happens with the option or stock after that.
The net result of this is that you’re committing to an effective cost basis that is well below what you’d have to pay if you just bought the stock on the open market today. In the previous example, the market price was $30.50, and you committed yourself to a $28.57 cost basis.
However, as many putselling tutorials will tell you, selling puts is “risky” because the downside risk outweighs the upside potential. The maximum rate of return you can get during this 3.5 months is a 5% return from put premiums. Your returns are therefore capped at 5%, or 18% annualized if you keep doing it. Your downside risk, however, is potentially very big. If the railroad were to suddenly go bankrupt and drop to $0/share, you’d be forced to buy them for $30/share, which would cost you $3,000. You’d at least get to keep your $143 premium to go out to a bar and buy drinks for your friends to cheer up.
Of course, if you simply had bought the railroad stock normally without any putselling, you’d be in the same position, except slightly worse. If you own any stock and it goes bankrupt, you can lose your entire investment. And in that case, you wouldn’t even have the $143 premium. Your friends would have to buy you drinks at the bar.
That’s why this strategy necessitates buying high quality companies. I prefer companies that pay dividends, companies that have economic moats, companies with a differentiated product or service, and companies that have weathered recessions in the past. Put selling is moderately more conservative than normal stock buying, but you still must pick high quality companies to minimize your downside risk.
I see people teaching different putselling strategies on more volatile, highrisk stocks with no intention to ever buy them, just to speculate with high premiums, and that’s not something I recommend for most people. I only suggest selling options on companies with a moat and a good balance sheet that you would actually like to own at the right price.
Put selling isn’t about hitting home runs. It’s about hitting a single or a double and getting to base almost every time. You either get paid a nice chunk of extra money for waiting to buy a stock you want at a lower price, or you get assigned to buy the stock at a low cost basis thanks to the option premium. It’s a tool that value investors can use to enter positions in great companies at great prices.
This chart shows the potential rate of returns of this option sale compared to buying the stock today at face value:
The horizontal axis gives a range of potential prices that the stock might be at during option expiration. The vertical axis indicates the rate of return over the lifetime of the option for each ending price, which was 3.5 months in this case. The pattern you see continues off the chart, from zero to infinity.
As you can see, upside potential is capped at 5% for the period (or 18% annualized), but your returns below that point are better than if you buy the stock outright.
Therefore, it’s a strategy not for when you’re extremely bullish, but for when you’re trying to buy the stock at a cheaper price, and when you’re trying to generate income and obtain some downside protection in an overvalued market.
A bullish LEAPS putselling example
A similar strategy to the above example is to sell longerterm put options that are in the money, meaning the strike price is above the current market price.
“LEAPS” stands for longterm equity anticipation securities. In other words, options that have an expiration date that is more than 12 months away.
The premiums for this type of option will be higher, and thus even though the strike price is higher than the market price, your cost basis if you buy the shares will be considerably lower than the market price.
There are a few main benefits of doing this type of option:
 Because it is in the money, it increases the odds of the option being exercised, while still giving you a lower cost basis on the purchased shares. Exercised options are often more taxefficient than expired options.
 If the option extends into the next calendar year, it will defer taxes for an entire year.
 It gives you a high upside cap, thus allowing you to be bullish, while still giving you downside protection compared to buying at the current market price.
 During periods of high volatility and high option premiums, you can sell these longterm options to “lock in” the high premiums. If instead you keep selling shortterm options, volatility may decrease during the rest of the year and give you lower premiums.
Here’s an example from when I originally wrote this article:
Put Table: 13 months until expiration
Click here for a bigger image.
This company engages in oil refining and owns a stake in an MLP for oil transport, currently trades for $29.20 per share, and pays a 4.5% dividend yield. Shares took a big price hit when oil prices collapsed in 2020, as refining margins decreased, and the stock had been roughly flat ever since.
Their balance sheet is strong, and Morningstar analysts are very bullish on the company and believe their fair value to be north of $40/share. OPEC agreed around this time to a deal to cut oil production, which has resulted in rising oil global prices, which should benefit this refiner in the long term by increasing their margins.
For this example, we’ll go with the option highlighted in red. If you sell that cashsecured put option for a strike price of $30, you’ll receive $5.50 in premiums per share, and it will expire in 13 months.
If it expires:
If the stock price goes up to over $30 by the time this expires, which is only a slight increase, then you’ll earn a 24% rate of return in 13 months and won’t be buying the shares. And you won’t pay taxes on these premiums until over a year after that.
If it is exercised:
On the other hand, if the stock price is under $30 by expiration, then you’ll buy at $30/share. Your cost basis including the premium will be just $24.50/share.
If you believe the company is fairlyvalued or undervalued, then this is a great investment in terms of risk and reward. You could make as much as 24% on your money in a year, and yet you also have considerable downside protection.
If the stock just stays flat all year at $29.20, you’ll buy it in 13 months at a cost basis of $24.50/share, for a rate of return of 19%.
The stock would have to drop a full 16% in price from $29.20 to $24.50 just for your investment to break even. Anything above that, and you make money.
And if the stock price drops a whopping 30%, down to $20.44/share, then your loss would be less than 17% on paper, since you will have paid $24.50 for shares that are now worth $20.44. At that point, if the fundamentals are still sound, you’ll be holding it and can collect dividends from it, so as long as you have a longterm view, you’ll likely do well as the price recovers.
Overall, this is an incredible option as long as you believe the company is a decent holding at around this price in the high $20’s. You can make marketbeating returns simply for the stock remaining flat or going up, and you have more than 10% downside protection in case it falls. You’re committing to a cost basis that is about 16% below the current market price.
The right option to sell depends on the scenario. If you’re trying to minimize fees and taxes, and trying to maximize downside protection, LEAPS puts can be the way to go. On the other hand, if you’re trying to maximize premiums, especially in nontaxed or deferredtax retirement accounts, shorterterm puts can give you a better return.
Final Words
Selling put options is one of the most flexible and powerful tools for generating income and entering stock positions.
Rather than buying shares at whatever the market currently offers, you can calculate exactly what you’re willing to pay for them, and then sell the put option to get paid to wait until it dips to that level.
This tactic is excellent for overvalued markets, as well as flat/bearish markets, because you can generate high returns even as the stock price stays flat or falls a bit, and can build 510% or more downside protection into your portfolio.
And while it’s not the perfect tactic for a strong bull market, it can be tailored to do reasonably well in that area as well, especially because you can tweak it by selling inthemoney options.
If you want more information, check out OptionWeaver. It’s a PDF booklet and excel calculator that helps you determine the fair value of stocks and figure out which options to sell.
It also includes a list of 50+ stocks and ETFs that I use as my baseline watchlist for selling options on. These are stocks and ETFs that meet all of the main criteria for being good securities for selling options on, and helps investors get started.
I also publish a free newsletter every 6 weeks or so that, in addition to updating readers on a variety of investing opportunities and economic information, often contains recent put options I’ve sold. Join here if you’re interested.
Basics Of Options Trading Explained
Before we delve deep into the world of options trading, let’s take a moment to understand why do we need options at all. If you are thinking it is just another way to make money and was created by some fancy guys in suits working in Wall Street, well, you are wrong. The options world predates the modern stock exchanges by a large margin.
While some credit the Samurai for giving us the foundation on which options contracts were based, some actually acknowledge the Greeks for giving us an idea on how to speculate on a commodity, in this case, the harvest of olives. In both cases, humans were trying to guess the price of a food item and trade accordingly (rice in the case of samurais), long before the modern world put in various rules and set up exchanges.
With this in mind, let us try to answer the first question in your mind.
What is options trading?
Let’s take a very simple example to understand options trading. Consider that you are buying a stock for Rs. 3000. But the broker tells you about an exciting offer, that you can buy it now for Rs. 3000 or you can give a token amount of Rs. 30 and reserve the right to buy it at Rs. 3000 after a month, even if the stock increases in value at that time. But that token amount is nonrefundable!
You realise that there is a high chance that the stock would cross Rs. 3030 and thus, you can breakeven at least. Since you have to pay only Rs. 30 now, the remaining amount can be used elsewhere for a month. You wait for a month and then look at the stock price.
Now, depending on the stock price, you have the option to buy the stock from the broker or not. Of course, this is an oversimplification but this is options trading in a gist.In the world of trading, options are instruments that belong to the derivatives family, which means its price is derived from something else, mostly stocks. The price of an option is intrinsically linked to the price of the underlying stock.
A formal definition is given below:
A stock option is a contract between two parties in which the stock option buyer (holder) purchases the right (but not the obligation) to buy/sell shares of an underlying stock at a predetermined price from/to the option seller (writer) within a fixed period of time.
We are going to make sure that by the end of this article you are well versed with the options trading world along with trying out a few options trading strategies as well. We will cover the following points in this article. If you feel that you want to skip the basics of options, then head straight to the options trading strategies.
Let’s start now, shall we!
Options trading vs. Stock trading
There must be a doubt in your mind that why do we even have options trading if it is just another way of trading. Well, here are a few points which make it different from trading stocks
 The Options contract has an expiration date, unlike stocks. The expiration can vary from weeks, months to years depending upon the regulations and the type of Options that you are practising. Stocks, on the other hand, do not have an expiration date.
 Unlike Stocks, Options derive their value from something else and that’s why they fall under the derivatives category
 Options are not definite by numbers like Stocks
 Options owners have no right (voting or dividend) in a company unlike Stock owners
It is quite often that some people find the Option’s concept difficult to understand though they have already followed it in their other transactions, for e.g. car insurance or mortgages. In this part of the article, we will take you through some of the most important aspects of Options trading before we get down to the world of options trading.
Options terminologies
Strike Price
The Strike Price is the price at which the underlying stocks can be bought or sold as per the contract. In options trading, the Strike Price for a Call Option indicates the price at which the Stock can be bought (on or before its expiration) and for Put Options trading it refers to the price at which the seller can exercise its right to sell the underlying stocks (on or before its expiration)
Premium
Since the Options themselves don’t have an underlying value, the Options premium is the price that you have to pay in order to purchase an Option. The premium is determined by multiple factors including the underlying stock price, volatility in the market and the days until the Option’s expiration. In options trading, choosing the premium is one of the most important components.
Underlying Asset
In options trading, the underlying asset can be stocks, futures, index, commodity or currency. The price of Options is derived from its underlying asset. For the purpose of this article, we will be considering the underlying asset as the stock. The Option of stock gives the right to buy or sell the stock at a specific price and date to the holder. Hence its all about the underlying asset or stocks when it comes to Stock in Options Trading.
Expiration Date
In options trading, all stock options have an expiration date. The expiration date is also the last date on which the Options holder can exercise the right to buy or sell the Options that are in holding. In Options Trading, the expiration of Options can vary from weeks to months to years depending upon the market and the regulations.
Options Style
There are two major types of Options that are practised in most of the options trading markets.
 American Options which can be exercised anytime before its expiration date
 European Options which can only be exercised on the day of its expiration
Moneyness (ITM, OTM & ATM)
It is very important to understand the Options Moneyness before you start trading in Stock Options. A lot of options trading strategies are played around the Moneyness of an Option.
It basically defines the relationship between the strike price of an Option and the current price of the underlying Stocks. We will examine each term in detail below.
When is an Option inthemoney?
 Call Option – when the underlying stock price is higher than the strike price
 Put Option – when the underlying stock price is lower than the strike price
When is an Option outofthemoney?
 Call Option – when the underlying stock price is lower than the strike price
 Put Option – when the underlying stock price is higher than the strike price
When is an Option atthemoney?
 When the underlying stock price is equal to the strike price.
Take a break here to ponder over the different terms as we will find it extremely useful later when we go through the types of options as well as a few options trading strategies.
Type of options
In the true sense, there are only two types of Options i.e Call & Put Options. We will understand them in more detail.
To Call or Put
A Call Option is an option to buy an underlying Stock on or before its expiration date. At the time of buying a Call Option, you pay a certain amount of premium to the seller which grants you the right (but not the obligation) to buy the underlying stock at a specified price (strike price).
Purchasing a call option means that you are bullish about the market and hoping that the price of the underlying stock may go up. In order for you to make a profit, the price of the stock should go higher than the strike price plus the premium of the call option that you have purchased before or at the time of its expiration.
In contrast, a Put Option is an option to sell an underlying Stock on or before its expiration date. Purchasing a Put Option means that you are bearish about the market and hoping that the price of the underlying stock may go down. In order for you to make a profit, the price of the stock should go down from the strike price plus the premium of the Put Option that you have purchased before or at the time of its expiration.
In this manner, both Put and Call option buyer’s loss is limited to the premium paid but profit is unlimited. The above explanations were from the buyer’s point of view. We will now understand the putcall options from the seller’s point of view, ie options writers. The Put option seller, in return for the premium charged, is obligated to buy the underlying asset at the strike price.
Similarly, the Call option seller, in return for the premium charged, is obligated to sell the underlying asset at the strike price. Is there a way to visualise the potential profit/loss of an option buyer or seller? Actually, there is. An option payoff diagram is a graphical representation of the net Profit/Loss made by the option buyers and sellers.
Before we go through the diagrams, let’s understand what the four terms mean. As we know that going short means selling and going long means buying the asset, the same principle applies to options. Keeping this in mind, we will go through the four terms.
 Short call – Here we are betting that the prices will fall and hence, a short call means you are selling calls.
 Short put – Here the short put means we are selling a put option
 Long call – it means that we are buying a call option since we are optimistic about the underlying asset’s share price
 Long put – Here we are buying a put option.
S = Underlying Price
X = Strike Price
Breakeven point is that point at which you make no profit or no loss.
The long call holder makes a profit equal to the stock price at expiration minus strike price minus premium if the option is in the money. Call option holder makes a loss equal to the amount of premium if the option expires out of money and the writer of the option makes a flat profit equal to the option premium.
Similarly, for the put option buyer, profit is made when the option is in the money and is equal to the strike price minus the stock price at expiration minus premium. And, the put writer makes a profit equal to the premium for the option.
All right, until now we have been going through a lot of theory. Let’s switch gears for a minute and come to the real world. How do options look like? Well, let’s find out.
What does an options trading quote consist of?
If you were to look for an options quote on Apple stock, it would look something like this:
When this was recorded, the stock price of Apple Inc. was $196. Now let’s take one line from the list and break it down further.
Eg.
In a typical options chain, you will have a list of call and put options with different strike prices and corresponding premiums. The call option details are on the left and the put option details are on the right with the strike price in the middle.
 The symbol and option number is the first column.
 The “last” column signifies the amount at which the last time the option was bought.
 “Change” indicates the variance between the last two trades of the said options
 “Bid” column indicates the bid submitted for the option.
 “Ask” indicates the asking price sought by the option seller.
 “Volume” indicates the number of options traded. Here the volume is 0.
 “Open Interest” indicates the number of options which can be bought for that strike price.
The columns are the same for the put options as well. In some cases, the data provider signifies whether the option is in the money, at the money or out of money as well. Of course, we need an example to really help our understanding of options trading. Thus, let’s go through one now.
Options Trading Example
We will go through two cases to better understand the call and put options.
For simplicity’s sake, let us assume the following:
 Price of Stock when the option is written: $100
 Premium: $5
 Expiration date: 1 month after the option is bought
Case 1:
The current price of stock: $110. Strike price: $120
Case 2:
The current price of stock: $120. Strike price: $110
Considering that we have gone through the detailed scenario of each option, how about we combine a few options together. Let’s understand an important concept which many professionals use in options trading.
What is PutCall Parity In Python?
Putcall parity is a concept that anyone who is interested in options trading needs to understand. By gaining an understanding of putcall parity you can understand how the value of call option, put option and the stock are related to each other. This enables you to create other synthetic position using various option and stock combination.
The principle of putcall parity
Putcall parity principle defines the relationship between the price of a European Put option and European Call option, both having the same underlying asset, strike price and expiration date. If there is a deviation from putcall parity, then it would result in an arbitrage opportunity. Traders would take advantage of this opportunity to make riskless profits till the time the putcall parity is established again.
The putcall parity principle can be used to validate an option pricing model. If the option prices as computed by the model violate the putcall parity rule, such a model can be considered to be incorrect.
Understanding PutCall Parity
To understand putcall parity, consider a portfolio “A” comprising of a call option and cash. The amount of cash held equals the call strike price. Consider another portfolio “B” comprising of a put option and the underlying asset.
S0 is the initial price of the underlying asset and ST is its price at expiration.
Let “r” be the riskfree rate and “T” be the time for expiration.
In time “T” the Zerocoupon bond will be worth K (strike price) given the riskfree rate of “r”.
Portfolio A = Call option + Zerocoupon bond
Portfolio B = Put option + Underlying Asset
If the share price is higher than X the call option will be exercised. Else, cash will be retained. Hence, at “T” portfolio A’s worth will be given by max(ST, X).
If the share price is lower than X, the put option will be exercised. Else, the underlying asset will be retained. Hence, at “T”, portfolio B’s worth will be given by max (ST, X).
If the two portfolios are equal at time, “T”, then they should be equal at any time. This gives us the putcall parity equation.
Equation for putcall parity:
C + XerT = P + S0
In this equation,
 C is the premium on European Call Option
 P is the premium of European Put Option
 S0 is the spot price of the underlying stock
 And, XerT is the current value (discounted value) of Zerocoupon bond (X)
We can summarize the payoffs of both the portfolios under different conditions as shown in the table below.
From the above table, we can see that under both scenarios, the payoffs from both the portfolios are equal.
Required Conditions For Putcall Parity
For putcall parity to hold, the following conditions should be met. However, in the real world, they hardly hold true and putcall parity equation may need some modifications accordingly. For the purpose of this blog, we have assumed that these conditions are met.
 The underlying stock doesn’t pay any dividend during the life of the European options
 There are no transaction costs
 There are no taxes
 Shorting is allowed and there are no borrow charges
Hence, putcall parity will hold in a frictionless market with the underlying stock paying no dividends.
Arbitrage Opportunity
In options trading, when the putcall parity principle gets violated, traders will try to take advantage of the arbitrage opportunity. An arbitrage trader will go long on the undervalued portfolio and short the overvalued portfolio to make a riskfree profit.
How to take advantage of arbitrage opportunity
Let us now consider an example with some numbers to see how trade can take advantage of arbitrage opportunities. Let’s assume that the spot price of a stock is $31, the riskfree interest rate is 10% per annum, the premium on threemonth European call and put are $3 and $2.25 respectively and the exercise price is $30.
In this case, the value of portfolio A will be,
C+XerT = 3+30e0.1 * 3/12 = $32.26
The value of portfolio B will be,
P + S0 = 2.25 + 31 = $33.25
Portfolio B is overvalued and hence an arbitrageur can earn by going long on portfolio A and short on portfolio B. The following steps can be followed to earn arbitrage profits.
 Short the stock. This will generate a cash inflow of $31.
 Short the put option. This will generate a cash inflow of $2.25.
 Purchase the call option. This will generate cash outflow of $3.
 Total cash inflow is 3 + 2.25 + 31 = $30.25.
 Invest $30.25 in a zerocoupon bond with 3 months maturity with a yield of 10% per annum.
Return from the zero coupon bond after three months will be 30.25e 0.1 * 3/12 = $31.02.
If the stock price at maturity is above $30, the call option will be exercised and if the stock price is less than $30, the put option will be exercised. In both the scenarios, the arbitrageur will buy one stock at $30. This stock will be used to cover the short.
Total profit from the arbitrage = $31.02 – $30 = $1.02
Well, shouldn’t we look at some codes now?
Python Codes Used For Plotting The Charts
The below code can be used to plot the payoffs of the portfolios.
So far, we have gone through the basic concepts in options trading and looked at an options trading strategy as well. At this juncture, let’s look at the world of options trading and try to answer a simple question.
Why is Options Trading attractive?
Options are attractive instruments to trade in because of the higher returns. An option gives the right to the holder to do something, with the ‘option’ of not to exercise that right. This way, the holder can restrict his losses and multiply his returns.
While it is true that one options contract is for 100 shares, it is thus less risky to pay the premium and not risk the total amount which would have to be used if we had bought the shares instead. Thus your risk exposure is significantly reduced.However, in reality, options trading is very complex and that is because options pricing models are quite mathematical and complex.
So, how can you evaluate if the option is really worth buying? Let’s find out.
The key requirement in successful options trading strategies involves understanding and implementing options pricing models. In this section, we will get a brief understanding of Greeks in options which will help in creating and understanding the pricing models.
Options Pricing
Options Pricing is based on two types of values
Intrinsic Value of an option
Recall the moneyness concept that we had gone through a few sections ago. When the call option stock price is above the strike price or when put option stock price is below the strike price, the option is said to be “InTheMoney (ITM)”, i.e. it has an intrinsic value. On the other hand, “Out of the money (OTM)” options have no intrinsic value. For OTM call options, the stock price is below the strike price and for OTM put options; stock price is above the strike price. The price of these options consists entirely of time value.
Time Value of an option
If you subtract the amount of intrinsic value from an options price, you’re left with the time value. It is based on the time to expiration. You can enroll for this free online options trading python course on Quantra and understand basic terminologies and concepts that will help you in options trading. We know what is intrinsic and the time value of an option. We even looked at the moneyness of an option. But how do we know that one option is better than the other, and how to measure the changes in option pricing. Well, let’s take the help of the greeks then.
Options Greeks
Greeks are the risk measures associated with various positions in options trading. The common ones are delta, gamma, theta and vega. With the change in prices or volatility of the underlying stock, you need to know how your options pricing would be affected. Greeks in options help us understand how the various factors such as prices, time to expiry, volatility affect the options pricing.
Delta measures the sensitivity of an option’s price to a change in the price of the underlying stock. Simply put, delta is that options greek which tells you how much money a stock option will rise or drop in value with a $1 rise or drop in the underlying stock. Delta is dependent on underlying price, time to expiry and volatility. While the formula for calculating delta is on the basis of the BlackScholes option pricing model, we can write it simply as,
Delta = [Expected change in Premium] / [Change in the price of the underlying stock]
Let’s understand this with an example for a call option:
We will create a table of historical prices to use as sample data. Let’s assume that the option will expire on 5th March and the strike price agreed upon is $140.
Thus, if we had to calculate the delta for the option on 2nd March, it would be $5/$10 = 0.5.
Here, we should add that since an option derives its value from the underlying stock, the delta option value will be between 0 and 1. Usually, the delta options creeps towards 1 as the option moves towards “inthemoney”.
While the delta for a call option increases as the price increases, it is the inverse for a put option. Think about it, as the stock price approaches the strike price, the value of the option would decrease. Thus, the delta put option is always ranging between 0 and 1.
Gamma measures the exposure of the options delta to the movement of the underlying stock price. Just like delta is the rate of change of options price with respect to underlying stock’s price; gamma is the rate of change of delta with respect to underlying stock’s price. Hence, gamma is called the secondorder derivative.
Gamma = [Change in an options delta] / [Unit change in price of underlying asset]
Let’s see an example of how delta changes with respect to Gamma. Consider a call option of stock at a strike price of $300 for a premium of $15.
 Strike price: $300
 Initial Stock price: $150
 Delta: 0.2
 Gamma: 0.005
 Premium: $15
 New stock price: $180
 Change in stock price: $180 – $150 = $30
Thus, Change in Premium = Delta * Change in price of stock = 0.2 * 30 = 6.
Thus, new premium = $15 + $6 = $21
Change in delta = Gamma * Change in stock price = 0.005 * 30 = 0.15
Thus, new delta = 0.2 + 0.15 = 0.35.
Let us take things a step further and assume the stock price increases another 30 points, to $210.
Now,
New stock price: $210
Change in stock price: $210 – $180 = $30
Change in premium = Delta *Change in 0.35*30 = $10.5
Thus, new premium = $21 + $10.5 = $31.5
Change in delta = Gamma * Change in stock price = 0.005 * 30 = 0.15
Thus, new delta = 0.35 + 0.15 = 0.5.
In this way, delta and gamma of an option changes with the change in the stock price. We should note that Gamma is the highest for a stock call option when the delta of an option is at the money. Since a slight change in the underlying stock leads to a dramatic increase in the delta. Similarly, the gamma is low for options which are either out of the money or in the money as the delta of stock changes marginally with changes in the stock option.
Highest Gamma for Atthemoney (ATM) option
Among the three instruments, atthemoney (ATM), outofthemoney (OTM) and inthemoney (ITM); at the money (ATM) has the highest gamma. You can watch this video to understand it in more detail.
Theta measures the exposure of the options price to the passage of time. It measures the rate at which options price, especially in terms of the time value, changes or decreases as the time to expiry is approached.
Vega measures the exposure of the option price to changes in the volatility of the underlying. Generally, options are more expensive for higher volatility. So, if the volatility goes up, the price of the option might go up to and viceversa.
Vega increases or decreases with respect to the time to expiry?
What do you think? You can confirm your answer by watching this video.
One of the popular options pricing model is Black Scholes, which helps us to understand the options greeks of an option.
BlackScholes options pricing model
The formula for the BlackScholes options pricing model is given as:
C is the price of the call option
P represents the price of a put option.
S0 is the underlying price,
X is the strike price,
σ represents volatility,
r is the continuously compounded riskfree interest rate,
t is the time to expiration, and
q is the continuously compounded dividend yield.
N(x) is the standard normal cumulative distribution function.
The formulas for d1 and d2 are given as:
To calculate the Greeks in options we use the BlackScholes options pricing model.
Delta and Gamma are calculated as:
In the example below, we have used the determinants of the BS model to compute the Greeks in options.
At an underlying price of 1615.45, the price of a call option is 21.6332.
If we were to increase the price of the underlying by Rs. 1, the change in the price of the call, put and values of the Greeks in the option is as given below.
As can be observed, the Delta of the call option in the first table was 0.5579. Hence, given the definition of the delta, we can expect the price of the call option to increase approximately by this value when the price of the underlying increases by Rs.1. The new price of the call option is 22.1954 which is
22.1954
22.1911
Let’s move to Gamma, another Greek in option.
If you observe the value of Gamma in both the tables, it is the same for both call and put options contracts since it has the same formula for both options types. If you are going long on the options, then you would prefer having a higher gamma and if you are short, then you would be looking for a low gamma. Thus, if an options trader is having a netlong options position then he will aim to maximize the gamma, whereas in case of a netshort position he will try to minimize the gamma value.
The third Greek, Theta has different formulas for both call and put options. These are given below:
In the first table on the LHS, there are 30 days remaining for the options contract to expire. We have a negative theta value of 0.4975 for a long call option position which means that the options trader is running against time.
He has to be sure about his analysis in order to profit from trade as time decay will affect this position. This impact of time decay is evident in the table on the RHS where the time left to expiry is now 21 days with other factors remaining the same. As a result, the value of the call option has fallen from 21.6332 to 16.9 behaviour 319. If an options trader wants to profit from the time decay property, he can sell options instead of going long which will result in a positive theta.
We have just discussed how some of the individual Greeks in options impact option pricing. However, it is very essential to understand the combined behaviour of Greeks in an options position to truly profit from your options position. If you want to work on options greeks in Excel, you can refer to this blog.
Let us now look at a Python package which is used to implement the Black Scholes Model.
Python Library – Mibian
What is Mibian?
Mibian is an options pricing Python library implementing the BlackScholes along with a couple other models for European options on currencies and stocks. In the context of this article, we are going to look at the BlackScholes part of this library. Mibian is compatible with python 2.7 and 3.x. This library requires scipy to work properly.
How to use Mibian for BS Model?
The function which builds the BlackScholes model in this library is the BS() function. The syntax for this function is as follows:
The first input is a list containing the underlying price, strike price, interest rate and days to expiration. This list has to be specified each time the function is being called. Next, we input the volatility, if we are interested in computing the price of options and the option greeks. The BS function will only contain two arguments.
If we are interested in computing the implied volatility, we will not input the volatility but instead will input either the call price or the put price. In case we are interested in computing the putcall parity, we will enter both the put price and call price after the list. The value returned would be:
(call price + price of the bond worth the strike price at maturity) – (put price + underlying asset price)
The syntax for returning the various desired outputs are mentioned below along with the usage of the BS function. The syntax for BS function with the input as volatility along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
The syntax for BS function with the input as callPrice along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
The syntax for BS function with the input as putPrice along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
The syntax for BS function with the inputs as callPrice and putPrice along with the list storing underlying price, strike price, interest rate and days to expiration:
Attributes of the returned value from the abovementioned BS function:
While BlackScholes is a relatively robust model, one of its shortcomings is its inability to predict the volatility smile. We will learn more about this as we move to the next pricing model.
Derman Kani Model
The Derman Kani model was developed to overcome the longstanding issue with the Black Scholes model, which is the volatility smile. One of the underlying assumptions of Black Scholes model is that the underlying follows a random walk with constant volatility. However, on calculating the implied volatility for different strikes, it is seen that the volatility curve is not a constant straight line as we would expect, but instead has the shape of a smile. This curve of implied volatility against the strike price is known as the volatility smile.
If the Black Scholes model is correct, it would mean that the underlying follows a lognormal distribution and the implied volatility curve would have been flat, but a volatility smile indicates that traders are implicitly attributing a unique nonlognormal distribution to the underlying. This nonlognormal distribution can be attributed to the underlying following a modified random walk, in the sense that the volatility is not constant and changes with both stock price and time. In order to correctly value the options, we would need to know the exact form of the modified random walk.
The Derman Kani model shows how to take the implied volatilities as inputs to deduce the form of the underlying’s random walk. More specifically a unique binomial tree is extracted from the smile corresponding to the random walk of the underlying, this tree is called the implied tree. This tree can be used to value other derivatives whose prices are not readily available from the market – for example, it can be used in standard but illiquid European options, American options, and exotic options.
What is the Heston Model?
Steven Heston provided a closedform solution for the price of a European call option on an asset with stochastic volatility. This model was also developed to take into consideration the volatility smile, which could not be explained using the Black Scholes model.
The basic assumption of the Heston model is that volatility is a random variable. Therefore there are two random variables, one for the underlying and one for the volatility. Generally, when the variance of the underlying has been made stochastic, closedform solutions will no longer exist.
But this is a major advantage of the Heston model, that closedform solutions do exist for European plain vanilla options. This feature also makes calibration of the model feasible. If you are interested in learning about these models in more detail, you may go through the following research papers,
 Derman Kani Model – “The Volatility Smile and Its Implied Tree” by Emanuel Derman and Iraj Kani.
 Heston Model – “A ClosedForm Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options”
So far, you have understood options trading and how to analyse an option as well as the pricing models used. Now, to apply this knowledge, you will need access to the markets, and this is where the role of a broker comes in.
Opening an options trading account
How to choose a broker for Options Trading?
Before we open an options trading account with a broker, let’s go over a few points to take into consideration when we choose a broker.
 Understand your aim when you tread the options trading waters, whether it is a way of hedging risk, as a speculative instrument, for income generation etc.
 Does the broker provide option evaluation tools of their own? It is always beneficial to have access to a plethora of tools when you are selecting the right option.
 Enquire the transaction costs or the commission charged by the broker as this will eat into your investment gains.
 Some brokers give access to research materials in various areas of the stock market. You can always check with the broker about access to research as well as subscriptions etc.
 Check the payment options provided by the broker to make sure it is compatible with your convenience.
Searching for the right broker
Once the required background research is done, you can choose the right broker as per your need and convenience. In the global market, a list of the top brokers is provided below:
List of Top International Brokers (Options Trading)
The list of top international options brokers is given below:
 Etrade ($0.65 per options contract)
 Ally Invest ($0.5 per contract traded)
 TD Ameritrade ($0.65 fee per contract)
 Interactive Brokers (starts at $0.25 per options contract)
 Schwab Brokerage ($0.65 per options contract)
List of Top Indian Brokers (Options Trading)
The list of top Indian options brokers is given below:
 Zerodha
 ICICI Direct
 HDFC Securites
 ShareKhan
 Kotak Securities
 Angel Broking
 Axis Direct
Great! Now we look at some options trading strategies which can be used in the real world.
Options Trading Strategies
There are quite a few options trading strategies which can be used in today’s trading landscape. One of the most popular options trading strategies is based on Spreads and Butterflies. Let’s look at them in detail.
Spreads and Butterflies
Spreads or rather spread trading is simultaneously buying and selling the same option class but with different expiration date and strike price. Spread options trading is used to limit the risk but on the other hand, it also limits the reward for the person who indulges in spread trading.
Thus, if we are only interested in buying and selling call options of security, we will call it a call spread, and if it is only puts, then it will be called a put spread.
Depending on the changing factor, spreads can be categorised as:
 Horizontal Spread – Different expiration date, Same Strike price
 Vertical Spread – Same Expiration date, Different Strike price
 Diagonal Spread – Different expiration date, Different Strike price
Remember that an option’s value is based on the underlying security (in this case, stock price). Thus, we can also distinguish an option spread on whether we want the price to go up (Bull spread) or go down (Bear spread).
Bull call spread
In a bull call spread, we buy more than one option to offset the potential loss if the trade does not go our way.
Let’s try to understand this with the help of an example.
The following is a table of the available options for the same underlying stock and same expiry date:
Normally, if we have done the analysis and think that the stock can rise to $200, one way would be to buy a call stock option with a strike price of $180 for a premium of $15. Thus, if we are right and the stock reaches $200 on expiry, we buy it at the strike price of $180 and pocket a profit of ($20 $15) = $5 since we paid the premium of $15.
But if we were not right and the stock price reaches $180 or less, we will not exercise the option resulting in a loss of the premium of $15. One workaround is to buy a call option at $180 and sell a call option for $200 at $10.
Thus, when the stock’s price reaches $200 on expiry, we exercise the call option for a profit of $5 (as seen above) and also pocket a profit of the premium of $10 since it will not be exercised by the owner. Thus, in this way, the total profit is ($5 + $10) = $15.
If the stock price goes above $200 and the put option is exercised by the owner, the increase in the profit from bought call option at $180 will be the same as the loss accumulated from the sold call option at $200 and thus, the profit would always be $15 no matter the increase in the stock price above $200 at expiry date.
Let’s construct a table to understand the various scenarios.
You can go through this informative blog to understand how to implement it in Python.
Bear put spread
The bull call spread was executed when we thought the stock would be increasing, but what if we analyse and find the stock price would decrease. In that case, we use the bear put spread.
Let’s assume that we are looking at the different strike prices of the same stock with the same expiry date.
One way to go about it is to buy the put option for the strike price of 160 at a premium of $15 while selling a put option for the strike price of $140 for the strike price of $10.
Thus, we create a scenario table as follows:
In this way, we can minimize our losses by simultaneously buying and selling options. You can go through this informative blog to understand how to implement it in Python.
Butterfly Spread
A butterfly spread is actually a combination of bull and bear spreads. One example of the Butterfly Options Strategy consists of a Body (the middle double option position) and Wings (2 opposite end positions).
 Its properties are listed as follows:
 It is a threeleg strategy
 Involves buying or selling of Call/Put options (unlike Covered Call Strategy where a stock is bought and an OTM call option is sold)
 Can be constructed using Calls or Puts
 4 options contracts at the same expiry date
 Have the same underlying asset
 3 different Strike Prices are involved (2 have the same strike price)
 Create 2 Trades with these calls
Other Trading Strategies
We will list down a few more options trading strategies below:
Summary
We have covered all the basics of options trading which include the different Option terminologies as well as types. We also went through an options trading example and the option greeks. We understood various options trading strategies and things to consider before opening an options trading account.
If you have always been interested in automated trading and don’t know where to start, we have created a learning track for you at Quantra, which includes the. “Trading using Option Sentiment Indicators” course.
Disclaimer: All data and information provided in this article are for informational purposes only. QuantInsti ® makes no representations as to accuracy, completeness, currentness, suitability, or validity of any information in this article and will not be liable for any errors, omissions, or delays in this information or any losses, injuries, or damages arising from its display or use. All information is provided on an asis basis.
How to Manage Expiring Options Positions
Tips for extending profits and reducing losses
As you well know, the third Friday of every month is known as “expiration Friday,” and I’d like to talk to you about how to manage your positions during this very active time for option traders.
Closing vs. Exercising
As an option buyer, whether calls or puts, you have right but not obligation when it comes to how you want to exit an option position. This means that, at any time during the life of your option contract, you can choose to either:
 Close your position and bank the profits or curtail your losses; or
 You can “exercise,” which means you tell your broker that you want to buy stock at the option strike (if it’s a call option) or sell shares at the strike (if it’s a put option).
Many people buy options with one of two intentions: They can become long (buy) a stock (if they bought a call) or “put” (sell) their existing long shares (if they bought a put) to someone else at the strike price of their respective options.
But remember, if you don’t want to wake up on the Monday morning after expiration with a stock position that you might or might not want (or that you may or may not be able to afford), you must instruct your broker beforehand that you do not want to exercise your option if it finishes inthemoney. Better yet, you can close the option (i.e., “sell to close”) directly. That way, as soon as your order is filled, the trade is completely shut down and you have nothing more to do with the option or the underlying stock.
However, what if that position was a profitable one and you simply ran out of time with your trade?
Rolling Your Option Position
When you are in a winning position, and it looks like the position is going to continue in your favor but time is running out due to expiration, you don’t have to say goodbye to your winning streak.
When you want to continue profiting from a position that’s moving in your favor, you have the ability to lock in your profits while exposing yourself to additional upside with a technique called “rolling.”
In fact, you don’t have to wait until expiration week to “roll.” If you’re sitting on a nice profit in an option that expires six months from now, there’s no reason why you should wait six months to close your position and risk losing out on all the gains you’ve made. When you roll, you bank your profits and use your original investment capital to buy another option in a furtherout expiration month. If the stock keeps rising, you can “roll up” your calls to a higher strike price, or “roll down” to a lower strike if you’re using puts. You can keep the momentum going for as long as your stock is running (or falling).
In other words, you have an incredible opportunity to lock in your profits and limit your risk, while maintaining the samesize position. When my stocktrader friends tell me how much better stocks are than options, I remind them about rolling to protect profits in a winning position and get situated for more profits (which you can’t do with any other security other than options). And I win that argument every time!
Rolling works for long options, but what about when you are selling options against a long stock (or option) position to generate income?
Expiration and Option Writers
When you sell options against your long stocks (or other long options) to collect premium while stocks are standing still or simply moving slowly, you do so to take advantage of time decay (i.e., the erosion of extrinsic value that happens most rapidly as expiration draws near). You will collect premium when you initiate the position (i.e., you “sell to open” the option). And, if the position works in your favor, the value of the option will decline.
I’m always surprised to hear option sellers debating whether to close the position before expiration (i.e., to “buy to close” the option) or to simply let it “expire worthless” if the position goes as expected and the option value declines.
First of all, if you are in a covered call position, it is a repetitive strategy that you do month after month. So, it shouldn’t be a problem to close out the expiring position before initiating the new one. However, if you aren’t planning to continue the position (I might ask, why not?), the risk of it NOT expiring worthless is why you close the position. Instead of watching and waiting for the option to expire, it’s best to buy it back. Chances are, you’ve gotten the lion’s share of the value out of the option, so it’s actually good to buy it back for a small loss.
Volatility tends to pick up during expiration week, as traders and investors take their old positions “off the board” and get repositioned in new expiration months and/or strikes. This could actually turn the price of your option in the wrong direction! If the stock is trading close to your option strike, you are taking a big risk in leaving your position to the fate of the expiration gods. The frontmonth, atthemoney strike options’ prices can change very quickly.
In other words, the option might be worth 10 cents now, but could shoot up to $1 going into expiration. That is risk you could have — and should have — removed from the table. This makes the case for not waiting until 3:59 p.m. Eastern on Friday to call your broker to close out!
Exercise vs. Assignment
Earlier, we talked about “exercise,” which is the buyer’s right — but the buyer is not obligated to exercise. So, who is obligated in the buyer/seller relationship?
It is the individual who sold the option who is obligated to fulfill the obligation that they got paid to take on.
With Americanstyle options (most equities), option buyers have the right to exercise their option at any time during the life of the contract; sellers get assigned when a buyer exercises. As we saw in our coveredcall example, the option seller was selling calls against a long stock position. You don’t ever want to be short options unless you have some type of hedge in case the position goes against you. The covered call strategy is best used on a stock that is in a slowgrinding uptrend. As the call writer, you can also profit if the stock stays still or even if it moves down a little bit.
However, if the call moves inthemoney at expiration (i.e., instead of declining in value, it starts gaining intrinsic value, or the amount by which it is inthemoney), you run the risk of having someone who bought that same option want to exercise it, which means that you as the seller would have to sell shares to them at the strike price.
The good news? You own the shares and can fulfill the obligation. The bad news? You’re out of your position!
Now, don’t blame your broker for taking you out of your position. It’s actually the Options Clearing Corp. (which guarantees both sides of a trade) that takes the people who are short that option and does a “random lottery” to determine who will fulfill the buyer’s obligation. To avoid assignment, you can buy back your short option at any time. If you needed another reason to close out your expiring options, remember that if your short option is inthemoney and you haven’t yet been assigned, you will be at expiration.
Expiration Does Not Mean Opportunity Runs Out
Options expiration sounds a lot scarier than it really is. Try to think of it in a more positive and realistic light: Expiration should serve as your reminder to “clean house” on your options account. You don’t have to watch the markets from momenttomoment for as long as they’re open, but it pays to check in more frequently than you would with your longerterm holdings.
As an options investor, you’re spending less money to control the samesized position in a stock to capture gains much more quickly than the traditional stock investor might ever be able to see. You don’t want to miss out on the opportunity to bank profits while you have them, to adjust losing positions while there’s still something left to work with, and to get repositioned for even better returns in the weeks and months to come.
When you think “expiration,” think “opportunities” to make more money.

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