Stock Evolution under Stochastic Volatility: A Discrete Approach

Abstract

This paper examines the pricing of options by approximating extensions of the Black--Scholes setup in which volatility follows a separate diffusion process. It generalizes the well--known binomial model, constructing a discrete two-- dimensional lattice. We discuss convergence issues extensively and calculate prices and implied volatilities for European-- and American--style put options. Keywords binomial model, option valuation, lattice approach, stochastic volatility JEL Classification G13 Stanford University, Hoover Institution, Stanford, CA 94305, U.S.A. email: [email protected] A Deutscher Akademischer Austauschdienst scholarship through HSP III (a joint program by the Federal and State Governments in Germany) is gratefully acknowledged. 1 Introduction In the setup of Samuelson (1965), Black and Scholes removed the intrinsic risk in a call option by continuous trading in the underlying stock and one bond; this has been the starting point for today's industry of pri..