ABSTRACT
In Chapter 8, we discuss methods of pricing derivatives using Monte Carlo simulation. The idea of Monte Carlo simulation is based on the law of large numbers and the fact that pricing derivatives can be reduced to the calculation of expected values of the pay-off under risk neutral measures. Thus, we must know how the underlying assets move under the risk neutral measure. Once the dynamics of the underlying assets under the risk neutral measure is given, the price of the derivative can be calculated. Monte Carlo simulation leads us to the approximate price of the derivative by generating random variables consistent with the risk neutral measure. We introduce various methods to improve the approximation such as variance reduction method including antithetic variate method and moment matching method. Finally, we show that Monte Carlo simulation is useful for calculating prices of exotic options and multi asset options.
