Options Arbitrage Explained

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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).

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.

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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.


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.

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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Arbitrage Betting Explained – The Ultimate Guide (2020)

In this article we explain all you need to know about Arbitrage betting. This includes exactly what it is and how it works, an example of an arbitrage bet, the pros and cons and more.

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Arbitrage Betting Explained

Arbitrage betting (also known as ‘surebets’), is one of the most talked about and controversial methods in sports betting.

It is a technique that has existed since the beginning of bookmaking. However, it has gained a significant increase in popularity over recent years due to the advances of technology and the rise of online bookmakers.

So, what exactly is arbitrage betting?

What Is Arbitrage Betting?

Arbitrage betting (‘Arbing’ for short) exploits opportunity to place proportionate bets on every possible outcome on the same event in order to guarantee a profit, regardless of the final result.

It is important to know the difference between arbitrage betting, which exploits odds and Matched Betting which exploits free bets.

Mathematically, Arbs occur when the odds available for all mutually exclusive outcomes of an event imply probabilities that add up to less than one. This may be due to:

  • A difference of opinion between bookmakers.
  • Promotions offers by bookmakers.
  • Errors made by bookmakers.

Arbitrage betting is 100% legal as the arber is simply exploiting price differences within the market. Understandably however, some online bookmakers do not like the concept and may therefore restrict or close the accounts of those they suspect of engaging in it.

Because of this, many arbers may decide to use betting exchanges who are not known for prohibiting customers. Betfair have one of the best and most popular online exchanges. For a full rundown of how it works and what it has to offer you can read our ultimate Betfair exchange review.

Arbitrage Bet Example

The best way for you to really grasp the idea of how arbitrage betting works is through an example.

To make things simple, we will use a tennis match between ‘Player 1′ and ‘Player 2′ and odds from ‘Bookmaker A’ and ‘Bookmaker B’. We will assume we have a betting bank of £100.

Bookmaker A Bookmaker B Arbitrage Opportunity
Player 1 1.25 1.44 1.44
Player 2 3.75 2.62 3.75
Bookmaker Margin 106.67 107.61 96.11%
Stake £27.75 £72.25 £100
Profit £4.00 £4.00

Note: Bookmaker’s Margin = (1/Decimal Odds Player 1)*100 + (1/Decimal Odds Player 2)*100

As you can see, by taking Bookmaker B’s odds on Player 1 (3.75) and Bookmaker A’s odds on Player 2 (1.44), the margin becomes in favour of the bettor and provides a guaranteed return of 3.89% (100-96.11).

So using the example above, the calculation would be as follows:

Once we have calculated the margin, we then need to ensure our stakes are in proportion to the odds. To do this, simply divide your total stake by the odds and then multiply this number by the profit margin.

So in this case, we would have to stake £72.25 on Player 1 (£100 ÷ 1.44 * 1.0389) and £27.75 on Player 2 (£100 ÷ 3.75 * 1.0389).

Therefore, with a total outlay of £100, we will grantee a profit of £4.00 regardless of which player wins.

Advantages Of Arbitrage Betting

  • Many arbers will have accounts with as many betting sites as possible and will switch between them. This ensures that bookmakers do not become suspicious or spot any patterns. If you can avoid being suspected, arbitrage betting can be profitable.
  • Fluctuations in odds mean that arbs may only be available for short periods. If you are able to monitor the market and quickly take advantage of opportunities then you can make consistent long term profits.

Disadvantages Of Arbitrage Betting

  • As mentioned earlier, bookmakers disapprove or any arbitrage techniques. Whilst it is not illegal, bookmakers will monitor people’s betting habits and trends. Should they be winning constantly or if they suspect you are arbing, they may close your account or suspend you. Alternatively they may simply limit your maximum stake.
  • Arbing is something that requires a lot of time and dedication. It also involves relatively large sums of money, given that 98% of opportunities return less than 1.2%.

3 Arbitrage Betting Tips

  1. Track Your Bets – Use a spreadsheet to keep a detailed record of your bets.
  2. Open Accounts – Create accounts with multiple bookmakers. Not only will you be able to take advantage of free bets and bonus sign up offers, but you can switch between sites and be less prone to being suspected.
  3. Always Check Your Bets – Ensure you are placing the right stakes on the right bets.

ThePuntersPage Final Say

Arbitrage betting is a technique used to cover all possible outcomes in order to grantee a profit, regardless of the final outcome.

Given that the typical return is between 2-5%, Arbing can be a rather tedious process and requires large stakes. However, if you have time, patience and dedication, it can be great long term investment.

How to exploit calendar arbitrage?

Say we are looking at European Call options in a toy environment with zero deterministic interest rates, a stock paying no dividends, no repo rates etc.

Let $C(T,K)$ be the price of a call with expiry $T$ and strike $K$ .

If for $T1 , $C(T1,K) > C(T2,K)$ then this is calendar arbitrage.

Please explain how should one exploit this arbitrage opportunity.

3 Answers 3

The answer by @HenriK is certainly correct. However, for justification, technique such as the Jensen inequality is needed. For example, since $x^+$ is a convex function, assuming zero interest and zero divdiend, \begin E\big((S_>-K)^+ \mid \mathcal_ \big) &\ge \big(E(S_> \mid \mathcal_)-K\big)^+\\ &=(S_-K)^+. \end That is, $C(T_2) – (S_-K)^+\ge 0$. Then, \begin C(T_2) – (S_-K)^+ + x > 0. \end

Alternatively, if we short the option with maturity $T_1$ and long the option with with maturity $T_2$, then we have the initial profit $x= C(T_1)-C(T_2) > 0$.

At time $T_1$, if $S_\le K$, the shorted option expires worthless, and then we have the total profit $(S_-K)^++x$.

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