Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach
We propose a model for the valuation of participating life insurance products under a generalized jump–diffusion model with a Markov-switching compensator. The Esscher transform is employed to determine an equivalent martingale measure in the incomplete market. The results are further manipulated through the utilization of the change of numeraire technique to reduce the dimensions of the pricing formulation. This paper is the first that extends the technique for a generalized jump–diffusion process with a Markov-switching kernel-biased completely random measure, which nests a number of important and popular models in finance. A numerical analysis is conducted to illustrate the practical implications.
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
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.:
- Grosen, Anders & Lochte Jorgensen, Peter, 2000. "Fair valuation of life insurance liabilities: The impact of interest rate guarantees, surrender options, and bonus policies," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 37-57, February.
- Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
- David Prieul & Vladislav Putyatin & Tarek Nassar, 2001. "On pricing and reserving with-profits life insurance contracts," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(3), pages 145-166.
- Davis, Mark H.A. & Johansson, Martin P., 2006. "Malliavin Monte Carlo Greeks for jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 101-129, January.
- Farzad Fard & Tak Siu, 2013. "Pricing and managing risks of European-style options in a Markovian regime-switching binomial model," Annals of Finance, Springer, vol. 9(3), pages 421-438, August.
- Bacinello, Anna Rita, 2001. "Fair Pricing of Life Insurance Participating Policies with a Minimum Interest Rate Guaranteed," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 31(02), pages 275-297, November.
- Albert Lo & Chung-Sing Weng, 1989. "On a class of Bayesian nonparametric estimates: II. Hazard rate estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(2), pages 227-245, June.
- 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.
- Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
- Anna Rita Bacinello, 2003. "Fair Valuation of a Guaranteed Life Insurance Participating Contract Embedding a Surrender Option," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(3), pages 461-487.
- Chi Chiu Chu & Yue Kuen Kwok, 2006. "Pricing Participating Policies With Rate Guarantees," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 517-532.
- 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.
- A. -M. Matache & P. -A. Nitsche & C. Schwab, 2005. "Wavelet Galerkin pricing of American options on Levy driven assets," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 403-424.
- Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux, 2001. "Applications of Malliavin calculus to Monte-Carlo methods in finance. II," Finance and Stochastics, Springer, vol. 5(2), pages 201-236.
- 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.
- 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.
- Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
- Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52.
When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:53:y:2013:i:3:p:712-721. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.