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Pricing Currency Options in Tranquil Markets: Modelling Volatility Frowns

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Author Info
G.C. Lim
G.M. Martin ()
V.L. Martin

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Abstract

Volatility smiles arise in currency option markets when empirical exchange rate returns distributions exhibit leptokurtosis. This feature of empirical distributions is symptomatic of turbulent periods when exchange rate movements are in excess of movements based on the assumption of normality. In contrast, during periods of tranquility, movements in exchange rates are relatively small, resulting in unconditional empirical returns distributions with thinner tails than the normal distribution. Pricing currency options during tranquil periods on the assumption of normal returns yields implied volatility frowns, with over-pricing at both deep-in and deep-out-of-the-money contracts and under-pricing for at-the-money contracts. This paper shows how a parametric class of thin-tailed distributions based on the generalized Student t family of distributions can price currency options during periods of tranquility.

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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 4/02.

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Length: 37 pages
Date of creation: May 2002
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Handle: RePEc:msh:ebswps:2002-4

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Related research
Keywords: Option pricing volatility frowns thin-tails generalized Student t.

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Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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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.:
  1. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  2. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May. [Downloadable!] (restricted)
    Other versions:
  3. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June. [Downloadable!] (restricted)
  5. 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 637-54, May-June. [Downloadable!] (restricted)
  6. Clement, E. & Gourieroux, C. & Monfort, A., 2000. "Econometric specification of the risk neutral valuation model," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 117-143. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Gael M. Martin & Catherine S. Forbes & Vance L. Martin, 2003. "Implicit Bayesian Inference Using Option Prices," Monash Econometrics and Business Statistics Working Papers 5/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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