A path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models

TL;DR

This paper introduces a path integral method to derive closed-form option pricing formulas, extending to stochastic volatility and interest rate models, and validates the approach with Monte Carlo simulations.

Contribution

It presents a novel path integral approach for deriving closed-form solutions in complex stochastic models, including stochastic volatility and interest rates.

Findings

Closed-form formulas derived for stochastic volatility models

Method extended to stochastic interest rate models

Validated formulas with numerical Monte Carlo simulations

Abstract

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our new analytical formulas are tested with numerical Monte Carlo simulations.