Compound option pricing under stochastic volatility

The aim of this paper is to propose a flexible and computationallyefficient lattice-based approximation for evaluating European and Americancompound options under stochastic volatility models. In comparison with theexisting evaluation procedures, the method is more flexible because it mayaccommodate several stochastic volatility specifications of the asset price process,and more efficient because it is computationally faster in computing accuratecompound option prices with respect to the benchmark. The method is obtainedas an extension of the Costabile et al. (2012) discretization, which consists inapproximating the stochastic volatility process by a recombining binomial lattice,and considers the asset value as an auxiliary variable whose dynamics is capturedby generating subsets of representative realizations to cover the range of possibleasset prices at each time slice. The backward induction scheme based on a linearinterpolation technique is adapted to compute both the underlying daughter optionand the compound option prices. Numerical experiments confirm the methodefficiency and accuracy.