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Risk Premium Impact in the Perturbative Black Scholes Model

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  • Luca Regis
  • Simone Scotti

Abstract

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 $\lambda$.

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File URL: http://arxiv.org/pdf/0806.0307
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Paper provided by arXiv.org in its series Papers with number 0806.0307.

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Date of creation: Jun 2008
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Handle: RePEc:arx:papers:0806.0307

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  1. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 50(2), pages 125-150, November.
  2. Christophe Pérignon & Christophe Villa, 2002. "Extracting Information from Options Markets: Smiles, State-Price Densities and Risk Aversion," European Financial Management, European Financial Management Association, European Financial Management Association, vol. 8(4), pages 495-513.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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  5. 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.
  6. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 6(3), pages 279-302.
  7. Stoll, Hans R & Whaley, Robert E, 1990. "Stock Market Structure and Volatility," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 3(1), pages 37-71.
  8. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, American Finance Association, vol. 51(5), pages 1611-32, December.
  9. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  10. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  11. 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, American Finance Association, vol. 40(2), pages 455-80, June.
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Cited by:
  1. Simone Scotti, 2010. "The impact of uncertainties on the pricing of contingent claims," Papers 1001.5202, arXiv.org.

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