Good-deal bounds in a regime-switching diffusion market

TL;DR

This paper develops a method to determine price bounds for derivatives in a regime-switching market, highlighting the impact of the Markov chain generator on these bounds, with practical calculations for European call options.

Contribution

It introduces a good-deal bounds approach to option pricing in incomplete regime-switching markets, emphasizing the generator's influence on pricing bounds.

Findings

Pricing bounds are highly sensitive to the Markov chain generator.

The method provides a range for European call options in incomplete markets.

Stability of bounds varies with generator modifications.

Abstract

We consider option pricing in a regime-switching diffusion market. As the market is incomplete, there is no unique price for a derivative. We apply the good-deal pricing bounds idea to obtain ranges for the price of a derivative. As an illustration, we calculate the good-deal pricing bounds for a European call option and we also examine the stability of these bounds when we change the generator of the Markov chain which drives the regime-switching. We find that the pricing bounds depend strongly on the choice of the generator.