HEDGING OPTIONS IN A DOUBLY MARKOV-MODULATED FINANCIAL MARKET VIA STOCHASTIC FLOWS

Tak Kuen Siu and Robert J. Elliott
Additional contact information
Robert J. Elliott: Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada3School of Commerce, University of South Australia, Adelaide, Australia

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 08, 1-41

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.

Keywords: Hedging; European options; filtering; doubly Markov-modulated models; stochastic flows; risk-minimizing hedging strategies (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.worldscientific.com/doi/abs/10.1142/S021902491950047X
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:22:y:2019:i:08:n:s021902491950047x

Ordering information: This journal article can be ordered from

DOI: 10.1142/S021902491950047X

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().