Exponential change of measure applied to term structures of interest rates and exchange rates
In this paper, we study the term structures of interest rates and foreign exchange rates through establishing a state-price deflator. The state-price deflator considered here can be viewed as an extension to the potential representation of the state-price density in [Rogers, L.C.G., 1997. The potential approach to the term structure of interest rates and foreign exchange rates. Mathematical Finance 7(2), 157-164]. We identify a risk-neutral probability measure from the state-price deflator by a technique of exponential change of measure for Markov processes proposed by [Palmowski, Z., Rolski, T., 2002. A technique for exponential change of measure for Markov processes. Bernoulli 8(6), 767-785] and present examples of several classes of diffusion processes (jump-diffusions and diffusions with regime-switching) to illustrate the proposed theory. A comparison between the exponential change of measure and the Esscher transform for identifying risk-neutral measures is also presented. Finally, we consider the exchange rate dynamics by virtue of the ratio of the current state-price deflators between two economies and then discuss the pricing of currency options.
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.
- Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
- Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
- John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005.
"A Theory Of The Term Structure Of Interest Rates,"
World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164
World Scientific Publishing Co. Pte. Ltd..
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
- Bakshi, Gurdip & Carr, Peter & Wu, Liuren, 2008. "Stochastic risk premiums, stochastic skewness in currency options, and stochastic discount factors in international economies," Journal of Financial Economics, Elsevier, vol. 87(1), pages 132-156, January.
- Bühlmann, Hans & Delbaen, Freddy & Embrechts, Paul & Shiryaev, Albert N., 1998. "On Esscher Transforms in Discrete Finance Models," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 28(02), pages 171-186, November.
- Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
- Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
- Nielsen, J. Aase & Klaus Sandmann, 1995. "Equity-linked life insurance - a model with stochastic interest rates," Discussion Paper Serie B 291, University of Bonn, Germany, revised Mar 1995.
- 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.
- Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
- L. C. G. Rogers, 1997. "The Potential Approach to the Term Structure of Interest Rates and Foreign Exchange Rates," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 157-176.
- Dijkstra, Theo K. & Yao, Yong, 2002. "Moment generating function approach to pricing interest rate and foreign exchange rate claims," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 163-178, October.
- Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:49:y:2011:i:2:p:216-225. 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: (Dana Niculescu)
If references are entirely missing, you can add them using this form.