Hedging options in a doubly Markov-modulated financial market via stochastic flows

Tak Kuen Siu*, Robert J. Elliott

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black-Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

Original languageEnglish
Article number1950047
Pages (from-to)1-41
Number of pages41
JournalInternational Journal of Theoretical and Applied Finance
Volume22
Issue number8
DOIs
Publication statusPublished - 20 Dec 2019

Keywords

  • doubly Markov-modulated models
  • European options
  • filtering
  • Hedging
  • risk-minimizing hedging strategies
  • stochastic flows

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