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The Pricing of Foreign Currency Options

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  • Angelo Melino
  • Stuart M. Turnbull

Abstract

This study examines the assumption that the exchange rate follows a log-normal probability distribution and it tests whether different stochastic specifications translate into important differences in implied option prices. The authors investigate a class of processes, which includes the log-normal probability distribution as a limiting case. None of the models perform particularly well. The main problem appears to be that the volatility estimates from actual exchange rate data are significantly smaller than those implied by observed option prices.

Suggested Citation

  • 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.
    • Handle: RePEc:cje:issued:v:24:y:1991:i:2:p:251-81
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    Citations

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    Cited by:

    1. McAleer, Michael & Wiphatthanananthakul, Chatayan, 2010. "A simple expected volatility (SEV) index: Application to SET50 index options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(10), pages 2079-2090.
    2. Anatoliy Swishchuk & Maksym Tertychnyi & Robert Elliott, 2014. "Pricing Currency Derivatives with Markov-modulated Levy Dynamics," Papers 1402.1953, arXiv.org.
    3. Lieu, Derming, 1997. "Estimation of empirical pricing equations for foreign-currency options: Econometric models vs. arbitrage-free models," International Review of Economics & Finance, Elsevier, vol. 6(3), pages 259-286.
    4. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    5. Gomes, Frederico Pechir & Takami, Marcelo Yoshio & Brandi, Vinicius Ratton, 2008. "Investigating Unusual Changes in Real-Dollar Exchange Rate," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 62(2), October.
    6. Shang-Jin Wei & Jeffrey A. Frankel, 1991. "Are Option-Implied Forecasts of Exchange Rate Volatility Excessively Variable?," NBER Working Papers 3910, National Bureau of Economic Research, Inc.
    7. Christian Bayer & Juho Happola & Ra'ul Tempone, 2017. "Implied Stopping Rules for American Basket Options from Markovian Projection," Papers 1705.00558, arXiv.org, revised Jun 2017.
    8. Vivek Bhargava & Robert Brooks & D. K. Malhotra, 2001. "Implied volatilities, stochastic interest rates, and currency futures options valuation: an empirical investigation," The European Journal of Finance, Taylor & Francis Journals, vol. 7(3), pages 231-246.
    9. Akihiko Takahashi & , Kota Takehara & Akira Yamazaki, 2006. "Pricing Currency Options with a Market Model of Interest Rates under Jump-Diffusion Stochastic Volatility Processes of Spot Exchange Rates," CIRJE F-Series CIRJE-F-451, CIRJE, Faculty of Economics, University of Tokyo.
    10. Ballestra, Luca Vincenzo & Cecere, Liliana, 2016. "A numerical method to estimate the parameters of the CEV model implied by American option prices: Evidence from NYSE," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 100-106.
    11. Akihiko Takahashi & Kota Takehara & Akira Yamazaki, 2006. "Pricing Currency Options with a Market Model of Interest Rates under Jump-Diffusion Stochastic Volatility Processes of Spot Exchange Rates," CARF F-Series CARF-F-082, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. Chen, Gang & Roberts, Matthew C. & Roe, Brian E., 2005. "Empirical Performance of Alternative Option Pricing Models for Commodity Futures Options," 2005 Annual meeting, July 24-27, Providence, RI 19183, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. 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.
    14. Melino, Angelo & Turnbull, Stuart M., 1995. "Misspecification and the pricing and hedging of long-term foreign currency options," Journal of International Money and Finance, Elsevier, vol. 14(3), pages 373-393, June.
    15. Padmakumari, Lakshmi & S., Maheswaran, 2017. "A new statistic to capture the level dependence in stock price volatility," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 355-362.
    16. Peter A. Abken & Saikat Nandi, 1996. "Options and volatility," Economic Review, Federal Reserve Bank of Atlanta, vol. 81(Dec), pages 21-35.
    17. Kim, Jerim & Kim, Bara & Moon, Kyoung-Sook & Wee, In-Suk, 2012. "Valuation of power options under Heston's stochastic volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1796-1813.
    18. Anatoliy Swishchuk & Maksym Tertychnyi & Winsor Hoang, 2014. "Currency Derivatives Pricing for Markov-modulated Merton Jump-diffusion Spot Forex Rate," Papers 1402.2273, arXiv.org.
    19. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    20. 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 (Revised in August 2007 and January 2009; subseq," CARF F-Series CARF-F-092, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.

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