Hybrid Equity Swap and Cap Pricing Under Stochastic Interest by Markov Chain Approximation

Abstract

Hybrid equity-rate derivatives are commonly traded between financial institutions, but are challenging to price with traditional methods. Especially challenging are those contracts which involve an explicit interest rate (fixing) dependence in the cashflows, which stretches typical measure-change approaches beyond their practical limit.

We introduce a framework for pricing equity swaps, equity cap/floors, and other hybrid derivatives under general stochastic short-rate models with a correlated equity. By utilizing the machinery of Continuous Time Markov Chain (CTMC) approximation, and a decoupled representation of the equity-rate model, we derive closed-form approximations for the hybrid contract prices based on a regime-switching model and prove theoretical convergence. The numerical implementation of the method is fast and very accurate, achieving superquadratic convergence in numerical experiments. The framework also provides a practical alternative to traditional approaches such as trees for pricing bonds and bond options under short-rates models which lack closed-form solutions.

Note: This is an older version of the work “Hybrid Equity Swap, Cap, and Floor Pricing Under Stochastic Interest by Markov Chain Approximation” by the same author.

Keywords: CTMC, markov chain approximation, stochastic interest, hybrid, equity, regime-switching, option pricing, bond option