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An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates

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  • Akihiko Takahashi
  • Kohta Takehara

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  • Akihiko Takahashi & Kohta Takehara, 2007. "An Asymptotic Expansion Approach to Currency Options with a Market Model of Interest Rates under Stochastic Volatility Processes of Spot Exchange Rates," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(1), pages 69-121, March.
    • Handle: RePEc:kap:apfinm:v:14:y:2007:i:1:p:69-121
    DOI: 10.1007/s10690-007-9054-9
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    References listed on IDEAS

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    1. Orlin Grabbe, J., 1983. "The pricing of call and put options on foreign exchange," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 239-253, December.
    2. Yoshifumi Muroi, 2005. "Pricing contingent claims with credit risk: Asymptotic expansion approach," Finance and Stochastics, Springer, vol. 9(3), pages 415-427, July.
    3. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    4. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method (Published in "Journal of Japan Statistical Society", Vol.35-2, 171-203, 2005. )," CARF F-Series CARF-F-030, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    5. Hilliard, Jimmy E. & Madura, Jeff & Tucker, Alan L., 1991. "Currency Option Pricing with Stochastic Domestic and Foreign Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(2), pages 139-151, June.
    6. Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
    7. Takao Kobayashi & Akihiko Takahashi & Norio Tokioka, 2003. "Dynamic Optimality of Yield Curve Strategies," International Review of Finance, International Review of Finance Ltd., vol. 4(1‐2), pages 49-78, March.
    8. Atsushi Kawai, 2003. "A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 49-74.
    9. Akihiko Takahashi & Kohta Takehara, 2007. "Fourier Transform Method with an Asymptotic Expansion Approach: an Application to Currency Options," CIRJE F-Series CIRJE-F-497, CIRJE, Faculty of Economics, University of Tokyo.
    10. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    11. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    12. Amin, Kaushik I & Bodurtha, James N, Jr, 1995. "Discrete-Time Valuation of American Options with Stochastic Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 8(1), pages 193-234.
    13. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    14. Naoto Kunitomo & Yong‐Jin Kim, 2007. "Effects Of Stochastic Interest Rates And Volatility On Contingent Claims," The Japanese Economic Review, Japanese Economic Association, vol. 58(1), pages 71-106, March.
    15. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    16. Kaushik I. Amin & Robert A. Jarrow, 2008. "Pricing foreign currency options under stochastic interest rates," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 14, pages 307-326, World Scientific Publishing Co. Pte. Ltd..
    17. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 06-83, Wharton School Rodney L. White Center for Financial Research.
    18. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    19. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
    20. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. "Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-430, March.
    21. Angelo Melino & Stuart M. Turnbull, 1991. "The Pricing of Foreign Currency Options," Canadian Journal of Economics, Canadian Economics Association, vol. 24(2), pages 251-281, May.
    22. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    23. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 6-83, Wharton School Rodney L. White Center for Financial Research.
    24. Naoto Kunitomo & Akihiko Takahashi, 2004. "Applications of the Asymptotic Expansion Approach based on Malliavin-Watanabe Calculus in Financial Problems," World Scientific Book Chapters, in: Jiro Akahori & Shigeyoshi Ogawa & Shinzo Watanabe (ed.), Stochastic Processes And Applications To Mathematical Finance, chapter 10, pages 195-232, World Scientific Publishing Co. Pte. Ltd..
    25. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    26. Mikkelsen, Peter, 2001. "Cross-Currency LIBOR Market Models," Finance Working Papers 01-6, University of Aarhus, Aarhus School of Business, Department of Business Studies.
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    Citations

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    Cited by:

    1. Akihiko Takahashi & Toshihiro Yamada, 2016. "An asymptotic expansion for forward-backward SDEs: a Malliavin calculus approach (Forthcoming in Asia-Pacific Financial Markets)," CARF F-Series CARF-F-394, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Akihiko Takahashi & Toshihiro Yamada, 2016. "An Asymptotic Expansion for Forward–Backward SDEs: A Malliavin Calculus Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 337-373, December.
    3. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(2), pages 147-182, May.
    4. Akihiko Takahashi & Toshihiro Yamada, 2016. "An Asymptotic Expansion for Forward-Backward SDEs: A Malliavin Calculus Approach," CIRJE F-Series CIRJE-F-1009, CIRJE, Faculty of Economics, University of Tokyo.

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