Compound option pricing under stochastic volatility

We develop a exible method for evaluating European and American compound options under stochastic volatilitymodels. After discretizing the volatility process by a recombining binomial lattice until the underlying optionexpiration, the method considers the asset value as an auxiliary variable and generates subsets of representativerealizations to cover the range of possible asset prices at each time slice. A backward induction scheme using alinear interpolation technique when required is then invoked to compute both the underlying daughter option andthe compound option prices. Numerical experiments conrm the method eciency and accuracy.