An extension of Heston's SV model to Stochastic Interest Rates

TL;DR

This paper extends Heston's stochastic volatility model to include stochastic interest rates by integrating a stochastic bond model, resulting in a semi-explicit option pricing formula.

Contribution

It introduces a novel extension of Heston's model that incorporates stochastic interest rates with minimal additional parameters, enabling semi-explicit valuation formulas.

Findings

Derived a semi-explicit formula for options with stochastic interest rates.

Extended Heston's model with a stochastic bond component.

Demonstrated the model's applicability to bond and currency options.

Abstract

In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula. Heston also describes, in general terms, how the model could be extended to incorporate Stochastic Interest Rates (SIR). This paper is devoted to the construction of an extension of Heston's SV model with a particular stochastic bond model which, just increasing in one the number of parameters, allows to incorporate SIR and to derive a semi-explicit formula for option pricing.