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Welcome to the Exotic

Option Fantasyland

Here you will find out how to price exotic options beyond your wildest dreams!

By Espen Haug


Welcome to the option fantasyland. At this page I will give you a short introduction to how you can construct and value options that looks very complex, but that not are that complex. The only limit will be your fantasy. Let me start by giving you a few simple examples:

 

MANHATTAN OPTION

Take a look at the figure to the left. I am sure you can see both the Empire state and the Chrysler building?


Actually the figure shows the payoff at expiration from what I call a Manhattan option. What will you sell me such an option for: 1$? Assume that stock A trades at 101, and stock B trades at 102.50. The volatility of asset A is 35% , the volatility of asset B is 25%. The risk-free rate is 5% and the expected correlation is 0.30. The time to maturity is 3 months.


This is not as complicated as it looks! Assuming the assets follows a geometric Brownian motion the value of the Manhattan option in this example must be 2.00$. If you sell it at1$ I will buy it from you!

 

PYRAMID OPTION

Have you ever been in Egypt. It probably took thousands of years building some of the nice Egyptian pyramids. But what about pricing a pyramid option?

Is it only fantasy or is it possible to value such an option. The answer is that also this option is quite simple to value. The trick is to understand that almost all types of complex payoff profiles can be built as a combination of more simple ones.

 

 

 

 

 

 

 
DIGITAL OPTIONS THE MOLECYLS OF OPTION PRICING

The figure to the left illustrates the payoff from a very simple option. The option pays a cash amount at maturity equal to K if asset one S1 at maturity is between level X1 and X2, and asset two S2 simultaneously is between X3 and X4. This is a simple type of two-asset digital option.


If you know how to price one of this you can just combine a lot of these together to engineer almost any option payoff profile you want. The formulas for this and several other digital/binary options can be found in: The Complete Guide to Option Pricing Formulas.


Most published formulas for digital/binary options assume geometric Brownian motion. But you could easily extend this approach to also working when assuming stochastic volatility, mean reverting, seasonallity or whatever process you prefer. It could be that you then not can find a closed form solution. In that case I would recommend you to take a close look at Quasi-Monte Carlo simulation.

Once again the only limit will be your fantasy. If you have a fantasy similar to mine that means no limits!

   

 
 

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