Asset Pricing in a Semi-Markov Modulated Market with Time-dependent Volatility

TL;DR

This paper extends the Black-Scholes model to a semi-Markov regime-switching market with time-dependent volatility, deriving an integral equation for option pricing in this complex setting.

Contribution

It introduces a semi-Markov regime-switching framework with time-dependent volatility for asset pricing, extending existing Markov models.

Findings

Derivation of an integral equation for option pricing

Extension of regime-switching models to semi-Markov processes

Incorporation of time-dependent volatility in asset pricing

Abstract

This project attempts to address the problem of asset pricing in a financial market, where the interest rates and volatilities exhibit regime switching. This is an extension of the Black-Scholes model. Studies of Markov-modulated regime switching models have been well-documented. This project extends that notion to a class of semi-Markov processes known as age-dependent processes. We also allow for time-dependence in volatility within regimes. We show that the problem of option pricing in such a market is equivalent to solving a certain integral equation.