Stochastic lattice models for valuation of volatility options

Abstract

In this paper an efficient stochastic lattice approach is developed to price the American-style volatility options on the general stochastic volatility models. The stochastic volatility diffusion models are first discretized into forms that are amenable for designing the lattice approach, then the paths of the underlying volatility are generated by the lattice, and finally the valuation of the American volatility options is realized by the backward processes. One of the keys to the designing of the lattice approach is to derive the probability distributions of the underlying volatility on the lattice-nodes. Numerical analysis is given to confirm the accuracy of the pricing methods. Also some empirical applications are provided in the paper.