Option trading arbitrage

Options arbitrage trades are commonly performed in the options market to earn small profits with very little or zero risk. Traders perform conversions when.
Table of contents

That is, at the same strike prices, a synthetic call should cost the same as an actual call. If this condition is violated, an opportunity for arbitrage exists. The arbitrage strategies we will be using in this article are:. Most option traders will probably never use these arbitrage strategies. But even if you don't trade these opportunities, understanding the mechanics of arbitrage and the relationships will make you a better trader and give you a new way of looking at options. Let's begin by looking at the first two, conversions and reversals, since these two strategies clearly show the relationship between the price of the underlying and the price of the put and call options.

The price of the put and call options across the same strike prices can not get very far out of line from the fair value dictated by the underlying price. As long as the risk and reward is the same, a synthetic call should cost the same as an actual call option. If it is not, then an arbitrage opportunity exists. You can buy the cheap one and sell the expensive one for a risk-free return. This is what the conversion strategy does.

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The long stock in the same amount specified in the options contract, shares in the case of most stock options plus the long put creates a long synthetic call. This is then offset by the actual short call option.


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This is a no-risk position. The potential return is simply based on the traded prices of all components. Another way to look at the conversion strategy is to group the option positions together and compare them to the underlying position. Combining the long put and short call create a synthetic short position in the underlying. The put makes money when the market drops and the call loses money when the market rises, so having the two option positions is just like being short the underlying. The conversion is completed, then, by buying the underlying, offsetting the synthetic short.

No matter how you look at it, you can see how puts, calls and the underlying asset are closely related. One value cannot move too far away from the other.

Watch on your big screen

The Graphic Analysis for most arbitrage strategies looks quite boring: A single horizontal line. In this case, the calls and puts for XYZ Corporation are fairly valued. However, if you found a case where the line was substantially above zero than the horizontal line would become quite exciting. If you could then actually execute the trade at those prices, it would mean you found a mispriced conversion, meaning a guaranteed profit with no risk! The reversal strategy is just the opposite of the conversion.

That is, you sell the underlying short and place a synthetic long position. The actual transactions needed would be:. Looking back at the table of synthetic relationships, you can see that it can again be grouped a different way. The short underlying position plus the long call is a synthetic long put option, which is then offset by the actual short put option. Again, there is no risk in this position. The only reason to do it is if you can buy the synthetic put for less than the bid price of the put you need to short.

This is just another example of the "buy low, sell high" theme that runs throughout the investing world, except that no time lapse is involved.


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You get to buy low and sell high at the same time. It is easy to get confused with these strategies, but remember the point of this section. It is to show how the calls, puts and underlying are related. The price of any one cannot move very far without the others adjusting as well. In addition to their relationship with the underlying asset, the price of each option is also related to the price of all the other options.

This theory says that the value of a call option implies a certain fair value for the corresponding put, and visa versa.

What Is Hedging, Speculation And Arbitrage?

Naturally, there are arbitrage strategies that are designed to profit if these relationships get out of line as well. You may have already guessed that the previously discussed conversions and reversals are two arbitrage strategies that could be used to take advantage of any mispricing in the relationship between puts and calls. But you can also do both of them! When you do a reversal at one strike price and a conversion at another all options in the same expiration month , the long and short positions in the underlying cancel out, and you are left with what is called a Box, an arbitrage strategy that uses four different options.

It is probably easiest to think of a box as doing both a bull spread and a bear spread. One spread is established using put options, and the other is established using call options. The spreads may both be debit spreads a bull call spread vs. Below is an example of one using the options in our hypothetical XYZ Corporation again. The risk graph is simply a horizontal line, just as all truly risk-free pure arbitrage trades would be.

The previous arbitrage strategies all used options within the same expiration month, and we have seen how the underlying and these options are related in one way or another.

What Is Hedging, Speculation And Arbitrage?

What about options from one expiration month to the next? Are there relationships between these as well? Yes, there are. Under normal circumstances, the implied volatility of the options in the farther-out months is a little higher than the front month. When that relationship is backwards, it may seem like a great trading opportunity. When traders see this happen they tend to think about placing calendar spreads that involve selling front month options and buying the farther-out options. The idea is to sell higher implied volatility and buy lower implied volatility, and then make money when the volatilities reverse themselves.

But there can be a problem with taking this route. Calendar spreads are typically market-neutral strategies that make money only if the stock stays in a narrow trading range. But keep in mind that implied volatility is the market's expectation of the magnitude of future stock price changes, and implied volatility that is higher in the front month than the back months is usually telling you something.

Volatility trading strategies

When you see implied volatility higher in the front month, there is almost always a reason for it. For example, it could be an upcoming earnings announcement, uncertainty regarding a particular sector, or an upcoming news item such as an FDA announcement. In those situations, the stock price could move up or down a great deal, depending on how the marketplace interprets the news or announcement. When a stock moves around a lot, market neutral trades are not necessarily going to be profitable, even if you sold high implied volatility and bought low implied volatility.

So when you see situations where the front month volatility is much higher than a farther out month, do some research before you enter any trade. You will probably find the reason why others are predicting wide short-term swings in the price of the stock. With that word of warning out of the way, let's show how the options of different months are related using an arbitrage strategy call a "jelly roll", sometimes simply called a roll.

To do this, we will again start with the conversion and reversal strategies. Consider the following reversal using our hypothetical XYZ Corporation:. It may be easier for you to think about this in the synthetic sense. You have a synthetic long stock position in the August options and a synthetic short stock position in the December options.

You are just spreading one month versus the other. If you are dealing with futures options, where these option months would be based on different futures month, then you are essentially just trading one month's value versus another. But when you are looking at a stock, this opens up some interesting issues. Think about what this position actually is. Once you reach the August expiration, you will be left with a long position in the stock.