A Taylor series approach to pricing and implied vol for LSV models

TL;DR

This paper introduces a Taylor series-based method for efficiently approximating prices and implied volatilities of European options within local-stochastic volatility models, avoiding complex computations.

Contribution

It provides a unified, explicit approximation framework for pricing and implied volatility that is computationally efficient and easy to implement.

Findings

Prices approximated using only the normal CDF

Implied volatilities computed explicitly without special functions

Method achieves near-instantaneous computation comparable to Black-Scholes

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 CDF 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.