Multiple Compound Option Price

Posted by Chun-Yuan Chiu

Multiple Compound Option Price

Input:
Initial underlying asset price
The 1st strike price
The 2nd strike price
The 3rd strike price
The 4th strike price
Time to maturity Years
Risk free interest rate (annulized)
Volatility (annulized)
Number of grid points
Window [-c, c], c =
Output:
Option value

This calculator gives the price of a multiple compound option (a call on call on call on call.) The calculation is based on the FFT method, which is capable of pricing n-fold compound options for arbitrary n, but in most cases in practice n=4 is enough. The algorithm is a sequence of operations on grid functions. We take uniform grid in the interval [-c, c]. For now the number of grid points can only be a power of 2.

The 4th strike price is the compound option's strike price at maturity date T. The 3rd strike price is the strike of the underlying call option at time t=3T/4, the 2nd one is the strike of the underlying call on call at t=2T/4, and the 1st one, the strike of the underlying call on call on call at t=T/4. Setting the first and the third strike prices to 0, this multiple compound option reduces to a call on a call. Setting the first three strike prices to 0, it reduces to a vanilla call option.

Tagged: FFT, Compound Option

 •  Mar 19, 2013  • 

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