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Accouting for Biases in Black-Scholes

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Author Info
David Backus (New York University)
Silverio Foresi (Goldman Sachs)
Liuren Wu (Fordham University)

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Abstract

Prices of currency options commonly differ from the Black-Scholes formula along two dimensions: implied volatilities vary by strike price (volatility smiles) and maturity (implied volatility of at­the­money options increases, on average, with maturity). We account for both using Gram­Charlier expansions to approximate the conditional distribution of the logarithm of the price of the underlying security. In this setting, volatility is approximately a quadratic function of moneyness, a result we use to infer skewness and kurtosis from volatility smiles. Evidence suggests that both kurtosis in currency prices and biases in Black­Scholes option prices decline with maturity.

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Paper provided by EconWPA in its series Finance with number 0207008.

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Length: 41 pages
Date of creation: 30 Aug 2002
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Handle: RePEc:wpa:wuwpfi:0207008

Note: Type of Document - postscript; prepared on MikTex; to print on postscript; pages: 41 ; figures: included. produced via dvips
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Related research
Keywords: currency options; skewness and kurtosis; Gram-Charlier expansions; implied volatility;

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
F31 - International Economics - - International Finance - - - Foreign Exchange
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods

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. 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.
    Other versions:
  2. Rosenberg, Joshua V., 1998. "Pricing multivariate contingent claims using estimated risk-neutral density functions," Journal of International Money and Finance, Elsevier, vol. 17(2), pages 229-247, April. [Downloadable!] (restricted)
    Other versions:
  3. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265. [Downloadable!] (restricted)
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  7. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
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  9. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November. [Downloadable!] (restricted)
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  12. Menachem Brenner & Young Ho Eom, 1997. "No-Arbitrage Option Pricing: New Evidence on the Validity of the Martingale Property," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-009, New York University, Leonard N. Stern School of Business-.
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  15. Akgiray, Vedat & Booth, G Geoffrey, 1988. "Mixed Diffusion-Jump Process Modeling of Exchange Rate Movements," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 631-37, November. [Downloadable!] (restricted)
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  18. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 1997. "Taming the Skew: Higher-Order Moments in Modeling Asset Price Processes in Finance," NBER Working Papers 5976, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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Full references

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. Angel León & Gonzalo Rubio, 2003. "Smiling under stochastic volatility," DFAEII Working Papers 200202, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
  2. Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA. [Downloadable!]
    Other versions:
  3. Stefano Galluccio & Yann Le Cam, 2005. "Implied Calibration of Stochastic Volatility Jump Diffusion Models," Finance 0510028, EconWPA. [Downloadable!]
  4. Liuren Wu, 2004. "Dampened Power Law: Reconciling the Tail Behavior of Financial Security Returns," Finance 0401001, EconWPA. [Downloadable!]
    Other versions:
  5. Peter Christoffersen & Sílvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO. [Downloadable!]
  6. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2001. "An Empirical Investigation of Continuous-Time Equity Return Models," NBER Working Papers 8510, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  7. David Backus & Silverio Foresi & Chris Telmer, 1998. "Discrete-Time Models of Bond Pricing," NBER Working Papers 6736, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  8. Gonzalo Rubio & Eva Ferreira & Mónica Gago, 2003. "An empirical comparison of the performance of alternative option pricing models," DFAEII Working Papers 200204, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
    Other versions:
  9. Terry Marsh & Takao Kobayashi, 2001. "The Contributions of Professors Fischer Black, Robert Merton, and Myron Scholes to the Financial Services Industry," CIRJE F-Series CIRJE-F-120, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
  10. Benjamin Miranda Tabak & Sandro Canesso de Andrade & Eui Jung Chang, 2004. "Tracking Brazilian Exchange Rate Volatility," Econometric Society 2004 Far Eastern Meetings 487, Econometric Society. [Downloadable!]
  11. Angel León & Gonzalo Rubio & Gregorio Serna, 2003. "Autorregresive conditional volatility, skewness and kurtosis," DFAEII Working Papers 200206, University of the Basque Country - Department of Foundations of Economic Analysis II. [Downloadable!]
  12. Gabriele Fiorentini & Angel León & Gonzalo Rubio, . "Short-term options with stochastic volatility: Estimation and empirical performance," Studies on the Spanish Economy 02, FEDEA. [Downloadable!]
    Other versions:
  13. 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!]
    Other versions:
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