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Simulation

We now consider using simulations to estimate the price of an option.

For a call option, this is to calculate the current expected value of

\begin{displaymath}\max(0,S_T-X) \end{displaymath}

or

\begin{displaymath}c_t = e^{-r(T-t)} E[\max(0,S_T-X)] \end{displaymath}

One way to estimate the value of the call is to simulate a large number of sample values of $S_T$ according to the assumed underlying process, and find the estimated call price as the average of the simulated values. By a Law of Large Numbers, this average will converge to the actual call value, where the rate of convergence will depend on the way we simulate the sample path, and how many simulations we perform.



Subsections
next up previous contents index
Next: Simulating the sample path. Up: Financial Numerical Recipes. Previous: American Options.   Contents   Index
Bernt Arne Odegaard
1999-09-09