A hidden Markov regime-switching model for option valuation
AbstractWe investigate two approaches, namely, the Esscher transform and the extended Girsanov's principle, for option valuation in a discrete-time hidden Markov regime-switching Gaussian model. The model's parameters including the interest rate, the appreciation rate and the volatility of a risky asset are governed by a discrete-time, finite-state, hidden Markov chain whose states represent the hidden states of an economy. We give a recursive filter for the hidden Markov chain and estimates of model parameters using a filter-based EM algorithm. We also derive predictors for the hidden Markov chain and some related quantities. These quantities are used to estimate the price of a standard European call option. Numerical examples based on real financial data are provided to illustrate the implementation of the proposed method.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Insurance: Mathematics and Economics.
Volume (Year): 47 (2010)
Issue (Month): 3 (December)
Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554
Option pricing Regime-switching Hidden Markov model Esscher transform Extended Girsanov principle Filters and predictors;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Goovaerts, Marc & Laeven, R., 2008.
"Actuarial risk measures for financial derivative pricing,"
Open Access publications from Katholieke Universiteit Leuven
urn:hdl:123456789/200996, Katholieke Universiteit Leuven.
- Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
- Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
- Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
- Naik, Vasanttilak, 1993. " Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-84, December.
- Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
- Marc J. Goovaerts & Rob Kaas & Roger J.A. Laeven & Qihe Tang, 2004.
"A Comonotonic Image of Independence for Additive Risk Measures,"
Tinbergen Institute Discussion Papers
04-030/4, Tinbergen Institute.
- Goovaerts, Marc J. & Kaas, Rob & Laeven, Roger J.A. & Tang, Qihe, 2004. "A comonotonic image of independence for additive risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 581-594, December.
- Laeven, R. & Kaas, R. & Goovaerts, Marc & Tang, Q., 2004. "A comonotone image of independence for additive risk measures," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/200581, Katholieke Universiteit Leuven.
- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
- Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
- Elliott, Robert J. & Hunter, William C. & Jamieson, Barbara M., 1998. "Drift and volatility estimation in discrete time," Journal of Economic Dynamics and Control, Elsevier, vol. 22(2), pages 209-218, February.
- Robert J. Elliott & Dilip B. Madan, 1998. "A Discrete Time Equivalent Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 127-152.
- Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
- X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor and Francis Journals, vol. 1(1), pages 38-44.
- Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wendy Shamier).
If references are entirely missing, you can add them using this form.