Pricing Path-dependent Options under Stochastic Volatility via Mellin Transform

TL;DR

This paper develops explicit formulas for pricing complex path-dependent options under stochastic volatility using Mellin transforms, validated through sensitivity analysis and Monte Carlo comparisons.

Contribution

It introduces a novel asymptotic approach with Mellin transform techniques to derive closed-form approximations for complex options under stochastic volatility.

Findings

Derived first-order approximation formulas for barrier and lookback options

Validated formulas through sensitivity analysis and Monte Carlo simulations

Demonstrated accuracy of the formulas for practical option pricing

Abstract

In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model, by using an asymptotic approach. To find the explicit closed-form formulas for the zero-order term and the first-order correction term, we use Mellin transform. We also conduct a sensitivity analysis on these formulas, and compare the option prices calculated by them with those generated by Monte-Carlo simulation.