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Pricing Multi-Asset Cross Currency Optionss

Author

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  • Kenichiro Shiraya

    (Graduate School of Economics, University of Tokyo)

  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

Abstract

This paper develops a general pricing method for multi-asset cross currency options, whose underlying asset consists of multiple different assets, and the evaluation currency is different from the ones used in the most liquid market of each asset; the examples include cross currency options, cross currency basket options and cross currency average options. We also demonstrate that our scheme is able to evaluate options with high dimensional state variables such as 200 dimensions, which is necessary for pricing basket options with 100 underlying assets under stochastic volatility environment. Moreover, in practice, fast calibration is necessary in the option markets relevant for the underlying assets and the currency, which is also achieved in this paper. Furthermore, we investigate the implied correlations in the cross currency markets on the dates before and after the events, Lehman Shock and Tohoku Earthquake .

Suggested Citation

  • Kenichiro Shiraya & Akihiko Takahashi, 2012. "Pricing Multi-Asset Cross Currency Optionss," CIRJE F-Series CIRJE-F-844, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2012cf844
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    References listed on IDEAS

    as
    1. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2012. "A General Computation Scheme for a High-Order Asymptotic Expansion Method," CARF F-Series CARF-F-272, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Paul Doust, 2012. "The Stochastic Intrinsic Currency Volatility Model: A Consistent Framework for Multiple FX Rates and Their Volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(5), pages 381-445, November.
    3. 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.
    4. Jean-Yves Datey & Genevieve Gauthier & Jean-Guy Simonato, 2003. "The Performance of Analytical Approximations for the Computation of Asian Quanto-Basket Option Prices," Multinational Finance Journal, Multinational Finance Journal, vol. 7(1-2), pages 55-82, March-Jun.
    5. Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
    6. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2012. "A General Computation Scheme For A High-Order Asymptotic Expansion Method," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-25.
    7. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CIRJE F-Series CIRJE-F-621, CIRJE, Faculty of Economics, University of Tokyo.
    8. Akihiko Takahashi & Kohta Takehara & Masashi Toda, 2009. "Computation in an Asymptotic Expansion Method," CARF F-Series CARF-F-149, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. 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.
    10. 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.
    11. Jörg Kienitz & Manuel Wittke, 2010. "Option Valuation in Multivariate SABR Models," Research Paper Series 272, Quantitative Finance Research Centre, University of Technology, Sydney.
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    Cited by:

    1. Akihiko Takahashi & Toshihiro Yamada, 2014. "On Error Estimates for Asymptotic Expansions with Malliavin Weights -Application to Stochastic Volatility Model- (Revised version of CARF-F-324; Forthcoming in "Mathematics of Operations Research," CARF F-Series CARF-F-347, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Sep 2014.
    2. Akihiko Takahashi & Yukihiro Tsuzuki, 2014. "A New Improvement Scheme for Approximation Methods of Probability Density Functions," CARF F-Series CARF-F-350, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    3. Akihiko Takahashi & Masashi Toda, 2012. "Note on an Extension of an Asymptotic Expansion Scheme," CIRJE F-Series CIRJE-F-860, CIRJE, Faculty of Economics, University of Tokyo.

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