A forward shooting grid method for option pricing with stochastic volatility

This article develops a forward shooting grid (FSG) method for pricing options on assets that evolve in a stochasticvolatility framework. We discretize the continuous evolution of the squared volatility (i.e., the path-independentstate variable) by a computationally simple binomial lattice; then the asset value (i.e., the path-dependent variable)is considered as an auxiliary state variable, and a subset of its possible realizations is attached to each node ofthe squared volatility lattice. The elements of the subset cover the range of possible asset prices at each timeslice, and linear interpolation is required when solving backward through the tree to find the initial value of thecontingent claim. The model is general to accommodate different specifications for both the squared volatilityand the asset price processes, and numerical experiments confirm that it is efficient and provides accurate results.