Compound option pricing under stochastic volatility

Abstract

The paper proposes a flexible and computationally efficient lattice-based approximation for evaluating European and American compound options under stochastic volatility models. In comparison with the existing evaluation procedures, the method is more flexible because it may accommodate several stochastic volatility specifications of the asset price process, and more efficient because it is computationally faster in computing accurate compound option prices. The method is obtained as an extension of Costabile et al. (2012) discretisation, which consists in approximating the stochastic volatility process by a recombining binomial lattice, and considers the asset value as an auxiliary variable whose dynamics is captured by generating subsets of representative realisations to cover the range of possible asset prices at each time slice. The backward induction scheme based on a linear interpolation technique is adapted to compute both the underlying daughter option and the compound option prices. Numerical experiments confirm the method efficiency and accuracy.