A Hidden Markov-Modulated Jump Diffusion Model for European Option Pricing

Tak Kuen Siu

Chapter Chapter 8 in Hidden Markov Models in Finance, 2014, pp 185-209 from Springer

Abstract: Abstract The valuation of a European-style contingent claim is discussed in a hidden Markov regime-switching jump-diffusion market, where the evolution of a hidden economic state process over time is described by a continuous-time, finite-state, hidden Markov chain. A two-stage procedure is used to discuss the option valuation problem. Firstly filtering theory is employed to transform the original market with hidden quantities into a filtered market with complete observations. Then a generalized version of the Esscher transform based on a Doléan-Dade stochastic exponential is employed to select a pricing kernel in the filtered market. A partial-differential-integral equation for the price of a European-style option is presented.

Keywords: Jump Diffusion Model; Esscher Transform; Markovian Regime-switching Models; Pricing Kernel; Hidden Markov Chain (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4899-7442-6_8

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