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Why Smiles Exist in Foreign Exchange Options Markets: Isolating Components of the Risk Neutral Process

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  • Robert Tompkins
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    Abstract

    Prices of foreign exchange options systematically diverge from those consistent with several previous option pricing models. This paper examines whether alternative models better explaining the empirical dynamics of the foreign exchange futures markets can yield implied volatility surfaces similar to those observed for options on Foreign Exchange futures. The most suitable alternative models include jumps and stochastic volatility. The inclusion of both these factors introduces unspanned sources of risk and therefore, the martingale measure will not necessarily be unique. However, it is not the objective of this research to propose which martingale measure is optimal; the aim, instead, is to gain a deeper understanding of the properties (and particularly the order of magnitude) of the risk premium. This is done by choosing a feasible martingale measure (based upon the no arbitrage condition), assuming no market price of jump or stochastic volatility risks, and price options under this measure. The implied volatility biases from model-based option prices are then compared to the actual implied volatility surfaces for options on these markets. The systematic and substantive differences that are found suggest a negative risk premium, which is a relatively more important (and universal) component in FX option pricing than previously reported. Furthermore, it appears that the relative risk premium across strike price and time is similar across four foreign exchange options markets. This may imply that some systematic mechanism causes the risk premium in these markets.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13518470500531150
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal The European Journal of Finance.

    Volume (Year): 12 (2006)
    Issue (Month): 6-7 ()
    Pages: 583-603

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    Handle: RePEc:taf:eurjfi:v:12:y:2006:i:6-7:p:583-603

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    Web page: http://www.tandfonline.com/REJF20

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    Related research

    Keywords: Stochastic volatility; normal inverse Gaussian distributions; methods of moments estimation; implied volatility smiles;

    References

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    1. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    2. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
    3. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 297-305, July.
    4. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    5. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
    6. 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.
    7. Ho, Mun S & Perraudin, William R M & Sorensen, Bent E, 1996. "A Continuous-Time Arbitrage-Pricing Model with Stochastic Volatility and Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 31-43, January.
    8. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    9. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
    10. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48.
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