Option Pricing and Filtering with Hidden Markov-Modulated Pure-Jump Processes

Robert J. Elliott and Tak Kuen Siu

Applied Mathematical Finance, 2013, vol. 20, issue 1, 1-25

Abstract: This article discusses the pricing of derivatives in a continuous-time, hidden Markov-modulated, pure-jump asset price model. The hidden Markov chain modulating the pure-jump asset price model describes the evolution of the hidden state of an economy over time. The market model is incomplete. We employ a version of the Esscher transform to select a price kernel for valuation. We derive a valuation formula for European options using a Fourier transform and the correlation theorem. This formula depends on the hidden Markov chain. It is then estimated using a robust filter of the chain.

Date: 2013
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DOI: 10.1080/1350486X.2012.655929

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