A Taylor Series Approach to Pricing and Implied Volatility for Local–Stochastic Volatility Models

Abstract

Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local–stochastic volatility setting. Our price approximations require only a normal cumulative distribution function and our implied volatility approximations are fully explicit (ie, they require no special functions, no infinite series and no numerical integration). As such, approximate prices can be computed as efficiently as Black– Scholes prices, and approximate implied volatilities can be computed nearly instantaneously.