Explicit implied volatilities for multifactor local-stochastic volatility models

TL;DR

This paper develops explicit asymptotic expansions for implied volatilities in multifactor local-stochastic volatility models, enabling accurate option pricing without complex computations across various models.

Contribution

It introduces a family of explicit asymptotic formulas for implied volatilities applicable to a wide range of local-stochastic volatility models, avoiding special functions and numerical integration.

Findings

High accuracy of the asymptotic expansions demonstrated across five models

Method's versatility shown through implementation on diverse dynamics

Explicit formulas simplify and speed up option pricing calculations

Abstract

We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under five different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility, $3/2$ stochastic volatility, and SABR local-stochastic volatility.