Spread option and exchange option with stochastic interest rates

TL;DR

This paper derives a closed-form solution for pricing exchange and spread options under stochastic interest rates, applicable to various models including Vasicek and CIR, and explores its use as a control variate.

Contribution

It provides a general closed-form formula for exchange options with stochastic interest rates, extending previous models and enabling improved spread option pricing.

Findings

Closed-form solution for exchange options with stochastic interest rates

Applicability to Vasicek, CIR, and other models

Potential use as control variate in spread option pricing

Abstract

In this work, we consider the issue of pricing exchange options and spread options with stochastic interest rates. We provide the closed form solution for the exchange option price when interest rate is stochastic. Our result holds when interest rate is modeled with a stochastic term structure of general form, which includes Vasicek model, CIR term structure, and other well-known term structure models as special cases. In particular, we have discussed the possibility of using our closed form solution as a control variate in pricing spread options with stochastic interest rate.