Hedging Options with Scale-Invariant Models
AbstractA price process is scale-invariant if and only if the returns distribution is independent of the price level. We show that scale invariance preserves the homogeneity of a pay-off function throughout the life of the claim and hence prove that standard price hedge ratios for a wide class of contingent claims are model-free. Since options on traded assets are normally priced using some form of scale-invariant process, e.g. a stochastic volatility, jump diffusion or Lévy process, this result has important implications for the hedging literature. However, standard price hedge ratios are not always the optimal hedge ratios to use in a delta or delta-gamma hedge strategy; in fact we recommend the use of minimum variance hedge ratios for scale-invariant models. Our theoretical results are supported by an empirical study that compares the hedging performance of various smile-consistent scale-invariant and non-scale-invariant models. We find no significant difference between the minimum variance hedges in the smile-consistent models but a significant improvement upon the standard, model-free hedge ratios
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Bibliographic InfoPaper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2006-03.
Length: 33 Pages
Date of creation: Jun 2006
Date of revision:
Publication status: Forthcoming in Journal of Banking and Finance
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Scale invariance; hedging; minimum variance; hedging; stochastic volatility;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
- Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
- David Heath & Eckhard Platen & Martin Schweizer, 2001. "A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 11(4), pages 385-413.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Geman, Hélyette, 2005. "From Measure Changes to Time Changes in Asset Pricing," Economics Papers from University Paris Dauphine 123456789/1388, Paris Dauphine University.
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, July.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
- Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
- Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
- 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.
- Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany.
- Latane, Henry A & Rendleman, Richard J, Jr, 1976. "Standard Deviations of Stock Price Ratios Implied in Option Prices," Journal of Finance, American Finance Association, vol. 31(2), pages 369-81, May.
- Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
- Bates, David S., 2005. "Hedging the smirk," Finance Research Letters, Elsevier, vol. 2(4), pages 195-200, December.
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