Question

You can:

- write an option 1: call option with an exercise price of PLN 100 and premium of PLN 5
- purchase an option 2: call option with an exercise price of PLN 140 and premium of PLN 5
- purchase an option 3: put option with an exercise price of PLN 100 and premium of PLN 3

Is an arbitrage possible? If yes, which options should be purchased in order to realize an arbitrage
strategy?

Answer 1

Answer

Yes arbitrage opportunity is available

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.

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.

In the above case

Buy option 3 and option 1