Approximate pricing of European and Barrier claims in a local-stochastic volatility setting

TL;DR

This paper develops asymptotic expansion methods to approximate prices of European and barrier options in complex local-stochastic volatility models, providing theoretical accuracy guarantees and numerical validation.

Contribution

It introduces a novel combination of Taylor series and correlation expansions for pricing in local-stochastic volatility models, with rigorous accuracy analysis.

Findings

Accurate asymptotic approximations for European options.

Numerical examples demonstrating effectiveness for barrier options.

Theoretical error bounds for European-style claim pricing.

Abstract

We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process. Rigorous accuracy results are provided for European-style claims. For barrier-style claims, we include several numerical examples to illustrate the accuracy and versatility of our approximations.