A general approach to option pricing by simulation.

In an earlier chapter we looked at estimation of an European call option price by simulation.

Estimation by simulation is in fact completely general, and can be used to approximate the price on any European derivative. It is not feasible to use simulation on American derivatives, because the optimal exercise policy needs to be known. If the form of this was known, there would be a closed form solution.

But for European derivatives simulation is feasible. For more ``exotic'' options simulation is often the only solution.

I will show how we can make a general framework for simulation of derivatives prices.

- Simulating prices of underlying.
- Defining payoffs.
- Pricing
- Improving the estimates, control variates.