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A Methodology for Assessing Model Risk and its Application to the Implied Volatility Function Model

Published online by Cambridge University Press:  06 April 2009

John Hull  and
Wulin Suo
John Hull
Affiliation:
[email protected], Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, M5S 3E6, Canada
Wulin Suo
Affiliation:
[email protected], School of Business, Queen's University, 99 University Avenue, Kingston, Ontario, K7L 3N6, Canada.
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Abstract

We propose a methodology for assessing model risk and apply it to the implied volatility function (IVF) model. This is a popular model among traders for valuing exotic options. Our research is different from other tests of the IVF model in that we reflect the traders' practice of using the model for the relative pricing of exotic and plain vanilla options at one point in time. We find little evidence of model risk when the IVF model is used to price and hedge compound options. However, there is significant model risk when it is used to price and hedge some barrier options.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 37 , Issue 2 , June 2002 , pp. 297 - 318
Copyright
Copyright © School of Business Administration, University of Washington 2002

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References

Andersen, L., and Andreasen, J.. “Factor Dependence of Bermudan Swaptions: Fact or Fiction.” Journal of Financial Economics, 62 (2001), 3–37.CrossRefGoogle Scholar
Andersen, L., and Brotherton-Ratcliffe, R.. “The Equity Option Volatility Smile: An Implicit Finite- Difference Approach.” Journal of Computational Finance, 1 (1998), 5–37.CrossRefGoogle Scholar
Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52 (1997), 2003–2049.CrossRefGoogle Scholar
Basel Committee on Banking Supervision. A New Capital Adequacy Framework. Basel, Switzerland: Bank for International Settlements (1999).Google Scholar
Bates, D. “Jumps and Stochastic Volatilities: Exchange Rate Processes Implicit in the Deutsche Mark Options.” Review of Financial Studies, 9 (1996), 69–107.CrossRefGoogle Scholar
Black, F., and Scholes, M. S.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–659.CrossRefGoogle Scholar
Boyle, P. P. “Options: A Monte Carlo Approach.” Journal of Financial Economics, 4 (1977), 323–338.CrossRefGoogle Scholar
Brace, A.; Goldys, B.; Klebaner, F.; and R.Womersley. “Market Model of Stochastic Implied Volatility with Application to the BGM Model.” Working Paper S01–1, Department of Statistics, Univ. of New South Wales (2001).Google Scholar
Britten-Jones, M., and Neuberger, A.. “Option Prices, Implied Price Processes, and Stochastic Volatility.” Journal of Finance, 55 (2000), 839–866.CrossRefGoogle Scholar
Broadie, M.; Glasserman, P.; and Kou, S. G.. “A Continuity Correction for Discrete Barrier Options.” Mathematical Finance, 7 (1997), 325–349.CrossRefGoogle Scholar
Buraschi, A., and Jackwerth, J.. “The Price of a Smile: Hedging and Spanning in Options Markets.” Review of Financial Studies, 14 (2001), 495–528.CrossRefGoogle Scholar
Derman, E. “Model Risk.” In Quantitative Strategies Research Notes. New York, NY: Goldman Sachs (1996).Google Scholar
Derman, E., and Kani, I.. “The Volatility Smile and its Implied Tree.” In Quantitative Strategies Research Notes. New York, NY: Goldman Sachs (1994).Google Scholar
Driessen, J.; Klaassen, P.; and Melenberg, B.. “The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions.” Working Paper, Department of Econometrics and CentER, Tilburg Univ. (2000).Google Scholar
Dumas, B.; Fleming, J.; and Whaley, R. E.. “Implied Volatility Functions: Empirical Tests.” Journal of Finance 53 (1998), 2059–2106.CrossRefGoogle Scholar
Dupire, B. “Pricing with a Smile.” Risk, 7 (1994), 18–20.Google Scholar
Geske, R. “The Valuation of Compound Options.” Journal of Financial Economics, 7 (1979), 63–82.CrossRefGoogle Scholar
Goldman, B.; Sosin, H.; and Gatto, M. A.. “Path Dependent Options: Buy at the Low, Sell at the High.” Journal of Finance, 34 (1979), 1111–1127.Google Scholar
Green, T. C., and Figlewski, S.. “Market Risk and Model Risk for a Financial Institution Writing Options.” Journal of Finance, 54 (1999), 1465–1499.CrossRefGoogle Scholar
Gupta, A., and Subrahmanyam, M. G.. “An Examination of the Static and Dynamic Performance of Interest Rate Models in the Dollar Cap-Floor Markets.” Working Paper, Weatherhead School of Management, Case Western Reserve Univ. (2000).Google Scholar
Heston, S. L. “A Closed-Form Solution for Options with Stochastic Volatility Applications to Bond and Currency Options.” Review of Financial Studies, 6 (1993), 327–343.CrossRefGoogle Scholar
Hull, J., and Suo, W.. “Modeling the Volatility Surface.” Working Paper, School of Business, Queens Univ. (2001).Google Scholar
Hull, J., and White, A.. “The Pricing of Options with Stochastic Volatility.” Journal of Finance, 42 (1987), 281–300.CrossRefGoogle Scholar
Hull, J., and White, A.. “An Analysis of the Bias in Option Pricing Caused by a Stochastic Volatility.” Advances in Futures and Options Research, 3 (1988), 27–61.Google Scholar
Hull, J., and White, A.. “Forward Rate Volatilities, Swap Rate Volatilities, and the Implementation of the LIBOR Market Model.” Journal of Fixed Income, 10 (2000) 46–62.CrossRefGoogle Scholar
Jackwerth, J. C., and Rubinstein, M.. “Recovering Probability Distributions from Option Prices.” Journal of Finance, 51 (1996), 1611–1631.CrossRefGoogle Scholar
Ledoit, O., and Santa-Clara, P.. “Relative Pricing of Options with Stochastic Volatility.” Working Paper, Anderson Graduate School of Management, Univ. of California, Los Angeles (1998).CrossRefGoogle Scholar
Longstaff, F. A.; Santa-Clara, P.; and Schwartz, E.. “Throwing away a Billion Dollars: The Cost of Suboptimal Exercise Strategies in the Swaptions Market.” Journal of Financial Economics, 62 (2001), 39–66.CrossRefGoogle Scholar
Melino, A., and Turnbull, S.M.. “Misspecification and the Pricing and Hedging of Long-Term Foreign Currency Options.” Journal of International Money and Finance, 14 (1995), 373–393.CrossRefGoogle Scholar
Merton, R. C. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4 (1973), 141–183.Google Scholar
Merton, R. C.. “Option Pricing when Underlying Returns are Discontinuous.” Journal of Financial Economics, 3 (1976), 125–144.CrossRefGoogle Scholar
Rosenberg, J. “Implied Volatility Functions: A Reprise.” Journal of Derivatives, 7 (2000), 51–64.CrossRefGoogle Scholar
Rubinstein, M. “Implied Binomial Trees.” Journal of Finance, 49 (1994), 771–818.CrossRefGoogle Scholar
Schöbel, R., and Zhu, J.. “Stochastic Volatility with an Ornstein-Uhlenbeck Process: An Extension.” Working Paper, Eberhard-Karls-Univ. Tübingen (1998).CrossRefGoogle Scholar
Stein, E., and Stein, C.. “Stock Price Distributions with Stochastic Volatility: An Analytical Approach.” Review of Financial Studies, 4 (1991), 727–752.CrossRefGoogle Scholar