Advanced Search
MyIDEAS: Login to save this article or follow this journal

Pricing currency options under two-factor Markov-modulated stochastic volatility models

Contents:

Author Info

  • Siu, Tak Kuen
  • Yang, Hailiang
  • Lau, John W.

Abstract

This article investigates the valuation of currency options when the dynamic of the spot Foreign Exchange (FX) rate is governed by a two-factor Markov-modulated stochastic volatility model, with the first stochastic volatility component driven by a lognormal diffusion process and the second independent stochastic volatility component driven by a continuous-time finite-state Markov chain model. The states of the Markov chain can be interpreted as the states of an economy. We employ the regime-switching Esscher transform to determine a martingale pricing measure for valuing currency options under the incomplete market setting. We consider the valuation of the European-style and American-style currency options. In the case of American options, we provide a decomposition result for the American option price into the sum of its European counterpart and the early exercise premium. Numerical results are included.

Download Info

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.
File URL: http://www.sciencedirect.com/science/article/B6V8N-4SGD4MJ-3/2/ace71802029146a500e9e13850c9432e
Download Restriction: Full text for ScienceDirect subscribers only

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.

Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 43 (2008)
Issue (Month): 3 (December)
Pages: 295-302

as in new window
Handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:295-302

Contact details of provider:
Web page: http://www.elsevier.com/locate/inca/505554

Related research

Keywords: Currency options Two-factor stochastic volatility Regime switching Esscher transform Decomposition;

References

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.:
as in new window
  1. 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.
  2. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
  3. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
  4. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  5. 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.
  6. Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
  7. Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
  8. 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.
  9. Johnson, Herb & Shanno, David, 1987. "Option Pricing when the Variance Is Changing," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(02), pages 143-151, June.
  10. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
  11. Schachermayer, W., 1992. "A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time," Insurance: Mathematics and Economics, Elsevier, vol. 11(4), pages 249-257, December.
  12. Back, Kerry & Pliska, Stanley R., 1991. "On the fundamental theorem of asset pricing with an infinite state space," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 1-18.
  13. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
  14. 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)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Anatoliy Swishchuk & Maksym Tertychnyi & Winsor Hoang, 2014. "Currency Derivatives Pricing for Markov-modulated Merton Jump-diffusion Spot Forex Rate," Papers 1402.2273, arXiv.org.
  2. Bo, Lijun & Wang, Yongjin & Yang, Xuewei, 2010. "Markov-modulated jump-diffusions for currency option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 461-469, June.
  3. Turinici, Gabriel & Papin, Timothée, 2013. "Valuation of the prepayment option of a perpetual corporate loan," Economics Papers from University Paris Dauphine 123456789/7818, Paris Dauphine University.
  4. Timothée Papin & Gabriel Turinici, 2012. "Prepayment option of a perpetual corporate loan: the impact of the funding costs," Working Papers hal-00768571, HAL.
  5. Timothée Papin & Gabriel Turinici, 2013. "Valuation of the Prepayment Option of a Perpetual Corporate Loan," Post-Print hal-00653041, HAL.
  6. Timothée Papin & Gabriel Turinici, 2014. "Prepayment option of a perpetual corporate loan: the impact of the funding costs," Post-Print hal-00768571, HAL.
  7. Bo, Lijun, 2011. "Exponential change of measure applied to term structures of interest rates and exchange rates," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 216-225, September.
  8. Papin, Timothée, 2013. "Pricing of Corporate Loan : Credit Risk and Liquidity cost," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/12545 edited by Turinici, Gabriel, September.
  9. Su, Xiaonan & Wang, Wensheng & Hwang, Kyo-Shin, 2012. "Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1777-1785.
  10. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2014. "Pricing foreign equity options with regime-switching," Economic Modelling, Elsevier, vol. 37(C), pages 296-305.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:295-302. 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: (Zhang, Lei).

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.