Hedging Options with Scale-Invariant Models
A 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
|Date of creation:||Jun 2006|
|Date of revision:|
|Publication status:||Forthcoming in Journal of Banking and Finance|
|Contact details of provider:|| Postal: PO Box 218, Whiteknights, Reading, Berks, RG6 6AA|
Phone: +44 (0) 118 378 8226
Fax: +44 (0) 118 975 0236
Web page: http://www.henley.reading.ac.uk/
More information through EDIRC
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.:
- 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.
- 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.
- 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.
- Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, September.
- 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.
- Robert C. Merton, 2005.
"Theory of rational option pricing,"
World Scientific Book Chapters,
in: Theory Of Valuation, chapter 8, pages 229-288
World Scientific Publishing Co. Pte. Ltd..
- 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.
- Bates, David S., 2005. "Hedging the smirk," Finance Research Letters, Elsevier, vol. 2(4), pages 195-200, December.
- Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
- Merton, Robert C., 1976.
"Option pricing when underlying stock returns are discontinuous,"
Journal of Financial Economics,
Elsevier, vol. 3(1-2), pages 125-144.
- Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany.
- 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.
- repec:dau:papers:123456789/1388 is not listed on IDEAS
- 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.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:rdg:icmadp:icma-dp2006-03. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marie Pearson)
If references are entirely missing, you can add them using this form.