Hedging options in a hidden Markov-switching local-volatility model via stochastic flows and a Monte-Carlo method

Robert J. Elliott, Tak Kuen Siu*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

The hedging of European contingent claims in a continuous-time hidden Markov-regime-switching diffusion model is discussed using stochastic flows of diffeomorphisms and Monte-Carlo simulations. Specifically, the price dynamics of an underlying risky asset are governed by a continuous-time hidden Markov-modulated local-volatility model. Filtering theory is used to estimate the unobservable drift given observable price information and to define a filtered market with complete observations. The delta–hedge ratio of a European option is derived using a martingale representation and stochastic flows of diffeomorphisms. The numerical computation of the delta–hedge ratio is estimated via Monte-Carlo simulations. Numerical results for illustrating the proposed method and the (relative) importance of the impacts of the information risk and the local-volatility parametrizations on the delta–hedge ratio are provided for the case of European call options.
Original languageEnglish
Pages (from-to)925-950
Number of pages26
JournalThe Journal of Futures Markets
Volume43
Issue number7
DOIs
Publication statusPublished - Jul 2023

Bibliographical note

© 2023 The Authors. The Journal of Futures Markets published by Wiley Periodicals LLC. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

  • filtering
  • hidden markov models
  • local volatility
  • Monte‐Carlo simulations
  • option hedging
  • stochastic flows

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