# 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
• 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, вЂњThe Relation Between Put and Call PricesвЂќ. 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, letвЂ™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 shouldnвЂ™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 canвЂ™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. ## Latency Arbitrage Explained ## Introduction: Latency arbitrage (LA) is a high-frequency trading strategy used to front run trading orders. Both institutional and retail traders are the victim of this predatory trading strategy. In this article I will explain this concept to you using a very simple analogy. As a trader it is very important to know the mechanics of the markets you trade. ## Explanation: For our example, latency will refer to the delay between your instructions and the time it takes for them to be executed. Imagine sitting in a room next to your best friend and sending them a text message? From the time you hit send until they receive the message will likely take a second, or two at most. This is latency ## Multiple Markets Example: Now let’s imagine you are looking to purchase 100 iPhones for your online Amazon store to stock up for the holiday season. You find out that you can purchase these phones across these wholesale stores: • Store A (5km away): 25 phones for$1,000
• Store B (10km away): 50 phones for $1,000 • Store C (15km away): 25 phones for$1,000

Here is a visual representation of the above scenario.

Latency Arbitrage Example

One thing you will notice is that these stores are actually increasingly further away in distance, but sell the phones for the same price.

So you jump in your car and drive to store A. Then store B. Finally, store C. Therefore, now you own all your phones and you are all set.

### Meet Mr. LA

Now imagine that a person named Latency Arbitrage (LA) decides they want to make some holiday money too. So LA waits at the closest store, store A – waiting to see if any big orders come in.

They talk to the clerk at store A and find out you are planning to buy 100 units and you are on your way to the store right now.

As a result, LA jumps in their Porsche to race to Store B and buys all 50 phones. Meanwhile, you are still on your way to Store A to purchase your first batch of 25 phones.

When you arrive at Store B, they are all out of stock.

LA meets you in the parking lot and says, hey, I got 50 phones for sale. Pay me $1,250 for them, I know you need them. What just happened? LA hiked the price on you because of their information and speed advantage. You got your phones but ended up paying more for them. Meanwhile LA made a pretty good return for a 5km drive. ## Stock Market Edition: This exact same example occurs in the stock market on a daily basis. Famous author Michael Lewis wrote a book to expose this malicious practice called Flashboys. Unfortunately, not many retail traders know that a market like “Nasdaq” routes orders to dozens of smaller exchages and dark pools. These high-frequency trading firms will pay the most money for a retail trader’s market order. As a result, the exchange generates more revenue. Using LA, orders are then “front-run” by using the speed advantage. This is the reason it costs millions of dollars to rent “office space” nearest to the exchange data centers. In fact, the exchanges themselves even rent out space in the very same building in which their computers route trading orders. What is even more astonishing is that over 60% of all market volume is now done by high frequency trading computers. But is this the root of the problem? ## High-Frequency Trading It is very important to note that not all high frequency trading is predatory latency arbitrage. In fact, high frequency trading through algorithms provides liquidity to the markets to help maintain an accurate market price of many assets. There is no issue with high technology deployed to re-balance portfolios efficiently. Heck, even to arbitrage the difference between two correlated assets. The problem arises when these powerful computers are coded to make money on the back of real traders looking to exchange shares. The real loser is the retail and institutional trader. Most importantly, the stock market is a tool for companies to raise capital from investors. Traders help this process by providing liquidity so there is always a buyer and seller ready to transact with. Latency arbitrage is just unfairly skimming off the top of these investors and traders. ## Defenses: Many companies have developed tool to fight latency arbitrage. They are slowing down the fastest orders, and creating high frequency programs to deliver an order to all exchanges at the same time. In response, latency arbitrage strategies are trying to get even faster to adapt to these defenses. As a result, it is a race of speed. #### As a retail trader your best defense is learning to read order flow like the professionals. In our futures day trading we share all the analytical and trading strategy tools to track the big orders, and profit using this information. Join our community and trade like the professionals, with the professionals. The PRO subscription includes the order flow trading course, live daily trading room and much more. The information contained in this post is solely for educational purposes, and does not constitute investment advice. The risk of trading in securities markets can be substantial. You should carefully consider if engaging in such activity is suitable to your own financial situation. TRADEPRO Academy is not responsible for any liabilities arising as a result of your market involvement or individual trade activities. ## Options Arbitrage Explained GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. #### Clone with HTTPS Use Git or checkout with SVN using the web URL. #### Downloading Want to be notified of new releases in JerBouma/Option-Arbitrage ? #### Launching GitHub Desktop If nothing happens, download GitHub Desktop and try again. #### Launching GitHub Desktop If nothing happens, download GitHub Desktop and try again. #### Launching Xcode If nothing happens, download Xcode and try again. #### Launching Visual Studio ## Latest commit ## Files Permalink Type Name Latest commit message Commit time Failed to load latest commit information. Options Arbitrage.csv Add files via upload Apr 1, 2020 Options Arbitrage.ipynb Add files via upload Apr 1, 2020 README.md Create README.md Apr 1, 2020 black_scholes.py Add files via upload Apr 1, 2020 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. • © 2020 GitHub, Inc. • Terms • Privacy • Security • Status • Help You can’t perform that action at this time. You signed in with another tab or window. Reload to refresh your session. You signed out in another tab or window. Reload to refresh your session. ## 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.

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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