Options Arbitrage Explained

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Contents

Options Arbitrage Strategies

In investment terms, arbitrage describes a scenario where it’s possible to simultaneously make multiple trades on one asset for a profit with no risk involved due to price inequalities.

A very simple example would be if an asset was trading in a market at a certain price and also trading in another market at a higher price at the same point in time. If you bought the asset at the lower price, you could then immediately sell it at the higher price to make a profit without having taken any risk.

In reality, arbitrage opportunities are somewhat more complicated than this, but the example serves to highlight the basic principle. In options trading, these opportunities can appear when options are mispriced or put call parity isn’t correctly preserved.

While the idea of arbitrage sounds great, unfortunately such opportunities are very few and far between. When they do occur, the large financial institutions with powerful computers and sophisticated software tend to spot them long before any other trader has a chance to make a profit.

Therefore, we wouldn’t advise you to spend too much time worrying about it, because you are unlikely to ever make serious profits from it. If you do want to know more about the subject, below you will find further details on put call parity and how it can lead to arbitrage opportunities. We have also included some details on trading strategies that can be used to profit from arbitrage should you ever find a suitable opportunity.

  • Put Call Parity & Arbitrage Opportunities
  • Strike Arbitrage
  • Conversion & Reversal Arbitrage
  • Box Spread
  • Summary

Put Call Parity & Arbitrage Opportunities

In order for arbitrage to actually work, there basically has to be some disparity in the price of a security, such as in the simple example mentioned above of a security being underpriced in a market. In options trading, the term underpriced can be applied to options in a number of scenarios.

For example, a call may be underpriced in relation to a put based on the same underlying security, or it could be underpriced when compared to another call with a different strike or a different expiration date. In theory, such underpricing should not occur, due to a concept known as put call parity.

The principle of put call parity was first identified by Hans Stoll in a paper written in 1969, “The Relation Between Put and Call Prices”. The concept of put call parity is basically that options based on the same underlying security should have a static price relationship, taking into account the price of the underlying security, the strike of the contracts, and the expiration date of the contracts.

When put call parity is correctly in place, then arbitrage would not be possible. It’s largely the responsibility of market makers,who influence the price of options contracts in the exchanges, to ensure that this parity is maintained. When it’s violated, this is when opportunities for arbitrage potentially exist. In such circumstances, there are certain strategies that traders can use to generate risk free returns. We have provided details on some of these below.

Strike Arbitrage

Strike arbitrage is a strategy used to make a guaranteed profit when there’s a price discrepancy between two options contracts that are based on the same underlying security and have the same expiration date, but have different strikes. The basic scenario where this strategy could be used is when the difference between the strikes of two options is less than the difference between their extrinsic values.

For example, let’s assume that Company X stock is trading at $20 and there’s a call with a strike of $20 priced at $1 and another call (with the same expiration date) with a strike of $19 priced at $3.50. The first call is at the money, so the extrinsic value is the whole of the price, $1. The second one is in the money by $1, so the extrinsic value is $2.50 ($3.50 price minus the $1 intrinsic value).

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The difference between the extrinsic values of the two options is therefore $1.50 while the difference between the strikes is $1, which means an opportunity for strike arbitrage exists. In this instance, it would be taken advantage of by buying the first calls, for $1, and writing the same amount of the second calls for $3.50.

This would give a net credit of $2.50 for each contract bought and written and would guarantee a profit. If the price of Company X stock dropped below $19, then all the contracts would expire worthless, meaning the net credit would be the profit. If the price of Company X stock stayed the same ($20), then the options bought would expire worthless and the ones written would carry a liability of $1 per contract, which would still result in a profit.

If the price of Company X stock went up above $20, then any additional liabilities of the options written would be offset by profits made from the ones written.

So as you can see, the strategy would return a profit regardless of what happened to the price of the underlying security. Strike arbitrage can occur in a variety of different ways, essentially any time that there’s a price discrepancy between options of the same type that have different strikes.

The actual strategy used can vary too, because it depends on exactly how the discrepancy manifests itself. If you do find a discrepancy, it should be obvious what you need to do to take advantage of it. Remember, though, that such opportunities are incredibly rare and will probably only offer very small margins for profit so it’s unlikely to be worth spending too much time look for them.

Conversion & Reversal Arbitrage

To understand conversion and reversal arbitrage, you should have a decent understanding of synthetic positions and synthetic options trading strategies, because these are a key aspect. The basic principle of synthetic positions in options trading is that you can use a combination of options and stocks to precisely recreate the characteristics of another position. Conversion and reversal arbitrage are strategies that use synthetic positions to take advantage of inconsistencies in put call parity to make profits without taking any risk.

As stated, synthetic positions emulate other positions in terms of the cost to create them and their payoff characteristics. It’s possible that, if the put call parity isn’t as it should be, that price discrepancies between a position and the corresponding synthetic position may exist. When this is the case, it’s theoretically possible to buy the cheaper position and sell the more expensive one for a guaranteed and risk free return.

For example a synthetic long call is created by buying stock and buying put options based on that stock. If there was a situation where it was possible to create a synthetic long call cheaper than buying the call options, then you could buy the synthetic long call and sell the actual call options. The same is true for any synthetic position.

When buying stock is involved in any part of the strategy, it’s known as a conversion. When short selling stock is involved in any part of the strategy, it’s known as a reversal. Opportunities to use conversion or reversal arbitrage are very limited, so again you shouldn’t commit too much time or resource to looking for them.

If you do have a good understanding of synthetic positions, though, and happen to discover a situation where there is a discrepancy between the price of creating a position and the price of creating its corresponding synthetic position, then conversion and reversal arbitrage strategies do have their obvious advantages.

Box Spread

This box spread is a more complicated strategy that involves four separate transactions. Once again, situations where you will be able to exercise a box spread profitably will be very few and far between. The box spread is also commonly referred to as the alligator spread, because even if the opportunity to use one does arise, the chances are that the commissions involved in making the necessary transactions will eat up any of the theoretical profits that can be made.

For these reasons, we would advise that looking for opportunities to use the box spread isn’t something you should spend much time on. They tend to be the reserve of professional traders working for large organizations, and they require a reasonably significant violation of put call parity.

A box spread is essentially a combination of a conversion strategy and a reversal strategy but without the need for the long stock positions and the short stock positions as these obviously cancel each other out. Therefore, a box spread is in fact basically a combination of a bull call spread and a bear put spread.

The biggest difficulty in using a box spread is that you have to first find the opportunity to use it and then calculate which strikes you need to use to actually create an arbitrage situation. What you are looking for is a scenario where the minimum pay out of the box spread at the time of expiration is greater than the cost of creating it.

It’s also worth noting that you can create a short box spread (which is effectively a combination of a bull put spread and a bear call spread) where you are looking for the reverse to be true: the maximum pay out of the box spread at the time of expiration is less than the credit received for shorting the box spread.

The calculations required to determine whether or not a suitable scenario to use the box spread exists are fairly complex, and in reality spotting such a scenario requires sophisticated software that your average trader is unlikely to have access to. The chances of an individual options trader identifying a prospective opportunity to use the box spread are really quite low.

Summary

As we have stressed throughout this article, we are of the opinion that looking for arbitrage opportunities isn’t something that we would generally advise spending time on. Such opportunities are just too infrequent and the profit margins invariably too small to warrant any serious effort.

Even when opportunities do arise, they are usually snapped by those financial institutions that are in a much better position to take advantage of them. With that being said, it can’t hurt to have a basic understanding of the subject, just in case you do happen to spot a chance to make risk free profits.

However, while the attraction of making risk free profits is obvious, we believe that your time is better spent identifying other ways to make profits using the more standard options trading strategies.

Forex Training Group

Arbitrage in the world of finance refers to a trading strategy that takes advantage of irregularities in a financial market. Forex arbitrage involves identifying and taking advantage of price discrepancies that can arise in the valuation of one or more currency pairs.

The general characteristic of real arbitrage is a “risk free” profit, but achieving this result usually involves taking a certain degree of risk during the execution of the trade. Often, the risk of execution actually exceeds the small profit that arbitrageurs commonly take in. A special type of arbitrage that does involve taking risk is known as statistical arbitrage where spreads between currency pairs are assessed and opposing positions taken when they get substantially out of line with historical norms.

While arbitrage trading is responsible for making large financial institutions and banks billions in profits, it has also been known to cause some of the largest financial collapses. This tends to occur when underlying parameters change and so the “risk free” profit in an arbitrage becomes instead a locked in loss. While arbitrage may appear like easy money for a forex trader, nothing could be further from the truth.

What is Arbitrage Trading in General?

Arbitrage can be defined as the simultaneous purchase and sale of two equivalent assets for a risk-free profit. In addition to the forex market, this trading strategy is actively employed in most financial markets, including the stock, commodity and options markets.

Basically, arbitrage takes advantage of discrepancies or irregularities in any given financial market, and involves situations where traders identify market conditions that allow them to take a small, risk-free profit when traded correctly. Forex arbitrage, as with arbitrage strategies in other markets, relies on these irregularities, which arise occasionally when markets trade inefficiently.

Arbitrage trade calculations, which were once done largely by hand or hand-held calculators, are now done in a number of way including forex arbitrage calculators, purpose made software programs, and even some trading platforms.

Because of the proliferation of such programs, financial markets have become even more efficient, which has further reduced the arbitrage opportunities in the forex market.

Several different methods can be used to arbitrage the forex market. For example, one such arbitrage technique involves buying and selling spot currency against the corresponding futures contract. Another form of currency arbitrage is called triangular arbitrage, which takes advantage of exchange rate discrepancies using three related currency pairs.

Other more complicated forms of forex arbitrage involve combining currency options, futures and spot; however, this type of arbitrage requires a significant initial margin deposit to execute since the selling of options is required. To add to the complexity of this type of arbitrage, a competent understanding of all three of those markets is imperative in the identification and execution of the arbitrage when it sets up.

Using a Forex Arbitrage System

Before the advent of computers, arbitrageurs operating at banks and other financial institutions would work out their numbers with a hand held calculator and a pencil. Nowadays, to accurately identify and act on irregularities in the forex market, a suitable software program that identifies and automatically executes trades is typically used instead.

For retail currency traders, this type of forex arbitrage program generally comes in the form of an Expert Advisor or EA that works within an advanced forex trading platform such as MetaTrader 4 or 5. The EA constantly watches the forex market, and when an opportunity for an FX arbitrage arises, the program automatically executes the trade. This greatly improves a trader’s chances of locking in an arbitrage profit and/or being able to take advantage of a fleeting opportunity.

Nevertheless, many traders feel uncomfortable with automatically executed trades and prefer to make their own trading decisions. Such traders generally use trade alert or signal software. This type of software, much like the expert advisor software, constantly scans the market, but instead of automatically executing the trades, it will alert the trader when an arbitrage situation arises. The trader can then decide whether or not to act.

Some traders that use their own arbitrage software programs may also subscribe to remote signal alert services. Used in conjunction with their own programs, these services alert the trader’s software when an arbitrage situation arises in the market. The trader’s software then either alerts the trader of the arbitrage or automatically executes the trades.

Currency Futures Arbitrage Basics

Because of interest rate differentials, currency futures tend to sell at a premium or at a discount, depending on how wide the interest rate differential is between the currencies of the two countries involved.

If the currency futures contract is for the Pound Sterling quoted against the U.S. Dollar, for example, and the pertinent interest rate in the UK is at two percent, while U.S. rates are at only one percent, then Sterling would trade at a forward discount relative to the spot rate.

This is due to the carrying cost differential of one percent since you would be better off buying Sterling spot and holding it until the value date than buying it forward against the Dollar.

The above figures will now be used to illustrate how a six-month futures contract for Sterling can be arbitraged against the spot market. First of all, the following market and contract parameters will be used:

  • The GBP/USD spot rate is trading at 1.2500.
  • The 6-month futures contract for GBP/USD is trading at 1.2400.
  • The 6-month interest rate on GBP is two percent.
  • The 6-month interest rate on USD is one percent.
  • The contract size is 1,000 units of currency.

The futures contract can be converted at the option of the seller of the contract into physical currency at the specified exchange rate when the futures contract matures in six months. The buyer of the 6-month GBP/USD futures contract would receive £1,000 and deliver $1,240 at the contract’s maturity in six months’ time.

The arbitrageur could then sell Sterling forward against the U.S. Dollar against the long futures contract. Alternatively, they could deposit £990.00 for six months at two percent. On the U.S. Dollar side, the trader would borrow $1,237 or the amount £990.00 would buy at the spot rate of 1.2500. A synthetic future would then be created converting £1,000 into $1,237 in six months’ time with a current cost of $1,237.

These numbers would indicate to an arbitrageur that the futures contract is trading slightly higher than it should be by three dollars per thousand. The arbitrage can then be established with the arbitrageur selling the futures contract for 1.2400 and buying spot with a net profit of $3.00 per thousand at the futures contract maturity. While $3.00 per thousand does not seem like a large profit on the trade, when the transaction is done in a large amount like $100,000,000, then the net profit would be a much more respectable $30,000.

Forex Triangular Arbitrage Explained

Many professional traders and market makers who specialize in cross currency pairs perform a process known as triangular arbitrage to lock in profits when the market driven cross rate temporarily deviates from the exchange rates observed for each component currency versus the U.S. Dollar. This popular currency arbitrage strategy takes advantage of the fact that the observed exchange rate for a cross currency pair is mathematically related to that of two other currency pairs.

Once the profit has been locked in by a triangular arbitrage, no further market risk exists. Nevertheless, the primary risk the cross currency trader still faces is counterparty risk, which would manifest into a significant problem if delivery on any leg of the three part transaction fails. Still, this risk is generally very low among well-established and creditworthy professional counterparties.

Traders performing a triangular arbitrage typically attempt to execute each leg of the three part transaction as simultaneously as possible. In addition to taking into account the costs of crossing any applicable bid off spreads to enter into the triangular arbitrage position, they also need to factor in their transaction costs to make sure they are locking in a profit.

Three currencies are involved in a triangular arbitrage, and traders use a mathematical formula to express the exchange rate for the cross currency pair as a function of the exchange rates for the two other related currency pairs that contain the U.S. Dollar as follows:

CCY2/CCY3 = USD/CCY3 x CCY2/USD

In the above equation, USD refers to the U.S. Dollar, while CCY2 is the base currency in the cross currency pair and CCY3 is the counter currency in the cross currency pair.

In addition, the term CCY2/CCY3 refers to the cross exchange rate of the counter currency CCY3 expressed in terms of the base currency or CCY2. The trader can also include any relevant transaction costs that may apply into computing an effective exchange rate.

The triangular arbitrageur performs the useful service of bring those markets back in line, and locks in a modest profit at the same time for their trouble. While retail forex traders rarely have this sort of opportunity, they can sometimes perform triangular arbitrages between the rates quoted by different online forex brokers.

Statistical Arbitrage in Forex Trading

In the forex market, statistical arbitrage involves seeking profit opportunities that arise from exchange rate discrepancies as determined by historical or predicted norms. Some traders prefer to call this spread trading rather than arbitrage because it does not technically result in locking in a risk-free profit as other true arbitrages do. Unlike other arbitrageurs operating in the forex market, statistical arbitrage traders therefore do actually take risk with their positions since the spreads between currency pairs that they seek to exploit can widen as well as narrow.

Most forex statistical arbitrage traders use mathematical modeling techniques and historical statistics consisting of the normal spreads between different currency pairs to determine which spreads are out of line and hence should see a narrowing over time. They will then endeavor to sell the overpriced currency pair and buy the underpriced currency pair.

If they do decide to engage in statistical arbitrage, a trader will also need to take some time to familiarize themselves with the mathematical and analytical methods used to identify such arbitrage opportunities. It may also be necessary for them to learn how to use and/or develop some computer systems to assist them in this process.

Choosing a Suitable Currency Arbitrage Strategy

Selecting the best FX currency arbitrage strategy to use for your particular situation and risk preference will probably depend on what markets you have access to, as well as whether or not you wish to take risk as an arbitrage trader.

For example, a professional cross currency trader and market maker will almost certainly be performing triangular arbitrage between their cross currency pair and the two other currency pairs that contain the same currencies quoted versus the U.S. Dollar. On the other hand, a trader with access to the currency futures market may instead wish to engage in futures arbitrage if they can deal in large enough amounts, have sufficiently small transaction costs and be able to identify arbitrage opportunities virtually in real time.

Finally, a retail forex trader with neither of those opportunities for arbitrage may be able to arbitrage quotes at different forex brokers to perform triangular arbitrage. Otherwise, they will probably be reduced to only having the ability to perform statistical arbitrage since they will most likely not have access to futures markets, Interbank pricing or clients dealing on their bid offer spreads. This also means their arbitrages will involve taking the risk of the spreads they perceive widening instead of narrowing based on their statistical analysis.

Another consideration when deciding whether to engage in arbitrage or what arbitrage strategy is right for you is that most arbitrages are done in as large a size as possible to maximize profits.

Accordingly, if you only have small transaction sizes to perform arbitrages with, then the proportionally modest potential income from this strategy may not interest you at all.

Forex Arbitrage Calculator Types

A concrete and popular example of a triangular arbitrate is often performed by professional EUR/JPY cross traders as part of their bread and butter business. When they see a large trade go through in any of the three related currency pairs of EUR/JPY, EUR/USD and USD/JPY, then the relationships between those markets gets sent briefly out of line as the big trade is assimilated into the exchange rates.

In particular, a EUR/JPY triangular arbitrage trader can readily enter the following transactions into an Excel spreadsheet to assist them in performing the following transactions in each currency pair to result in a locked in profit:

  • Buy 1,000,000 EUR/USD at 1.1500

= Long 1,000,000 Euros and Short 1,150,000 U.S. Dollars

  • Sell 1,000,000 EUR/JPY at 130.00

= Short 1,000,000 Euros and Long 130,000,000 Japanese Yen

  • Buy 1,150,000 USD/JPY at 113.00

= Long 1,150,000 U.S. Dollars and Short 129,950,000 Yen

  • Net Position or Profit

= Long 50,000 Yen at a rate of 113.00 for USD/JPY = US$442.48

When a retail trader is attempting to perform a triangular arbitrage between different online brokers, they can use an online arbitrage calculator like the one on the Forexop website that is shown in the screenshot image below. The same website also has an online calculator that helps you determine whether profitable futures versus spot arbitrage opportunities may exist.

Using an Arbitrage Trading Program

An arbitrage trading program or ATP consists of computer software that can be used by a forex trader to enter orders simultaneously for spot, cross rate and currency futures contracts. This sort of software is usually employed by institutional or bank traders and involves executing large volume transactions in order to maximize arbitrage profits.

When involving futures arbitrage, the arbitrage trading program will enter either a long or a short position on an exchange traded futures contract, while the other order will involve taking the opposite position in the forex spot market or with an online forex broker.

Arbitrage trading programs are a form of program or algorithmic trading which involves the execution of trades in financial markets by automated computer programs. These programs follow a set of predetermined rules or algorithms when executing trades based one an identified opportunity to profit from an existing arbitrage between markets.

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Options Arbitrage Explained

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This repository includes the Notebook, which entails identifying arbitrage opportunities and acting on them, a seperate Python file used to perform the Black Scholes calculations and a datafile.

The options and stocks can be mispriced relative to each other (Black Scholes), and if you trade on this arbitrage correctly there is (small) margin to be made. Arbitrage options trading is a market-neutral strategy that seeks to neutralize certain market risks by taking offsetting long and short related securities.

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