Risk Premium Impact in the Perturbative Black Scholes Model
We study the risk premium impact in the Perturbative Black Scholes model. The Perturbative Black Scholes model, developed by Scotti, is a subjective volatility model based on the classical Black Scholes one, where the volatility used by the trader is an estimation of the market one and contains measurement errors. In this article we analyze the correction to the pricing formulas due to the presence of an underlying drift different from the risk free return. We prove that, under some hypothesis on the parameters, if the asset price is a sub-martingale under historical probability, then the implied volatility presents a skewed structure, and the position of the minimum depends on the risk premium $\lambda$.
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.:
- Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302.
- 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.
- Stoll, Hans R & Whaley, Robert E, 1990. "Stock Market Structure and Volatility," Review of Financial Studies, Society for Financial Studies, vol. 3(1), pages 37-71.
- George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2009.
"Mispricing of S&P 500 Index Options,"
Review of Financial Studies,
Society for Financial Studies, vol. 22(3), pages 1247-1277, March.
- Jens Carsten Jackwerth & George M. Constantinaides & Stylianos Perrakis, 2005. "Mispricing of S&P 500 Index Options," CoFE Discussion Paper 05-09, Center of Finance and Econometrics, University of Konstanz.
- Stylianos Perrakis & Jens Carsten Jackwerth & George Constantinides, 2005. "Mispricing of S&P 500 Index Options," Working Papers wp05-07, Warwick Business School, Finance Group.
- George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2008. "Mispricing of S&P 500 Index Options," NBER Working Papers 14544, National Bureau of Economic Research, Inc.
- Nicolas Bouleau, 2003. "Error Calculus and Path Sensitivity in Financial Models," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 115-134.
- Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
- 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.
- Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
- Christophe Pérignon & Christophe Villa, 2002. "Extracting Information from Options Markets: Smiles, State-Price Densities and Risk Aversion," European Financial Management, European Financial Management Association, vol. 8(4), pages 495-513.
- Rubinstein, Mark, 1985. " Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-80, June.
- Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
When requesting a correction, please mention this item's handle: RePEc:arx:papers:0806.0307. 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: (arXiv administrators)
If references are entirely missing, you can add them using this form.