Option pricing and filtering with hidden Markov-modulated pure-jump processes

Robert J. Elliott, Tak Kuen Siu

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalApplied Mathematical Finance
Volume20
Issue number1
DOIs
Publication statusPublished - Mar 2013

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