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Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows

Author

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  • TAK KUEN SIU

    (Department of Actuarial Studies and Business Analytics, Macquarie Business School, Macquarie University, Sydney, NSW 2109, Australia)

  • ROBERT J. ELLIOTT

    (Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada3School of Commerce, University of South Australia, Adelaide, Australia)

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.

Suggested Citation

  • Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:08:n:s021902491950047x
    DOI: 10.1142/S021902491950047X
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