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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 $\lambda$.

Suggested Citation

  • Luca Regis & Simone Scotti, 2008. "Risk Premium Impact in the Perturbative Black Scholes Model," Papers 0806.0307, arXiv.org.
    • Handle: RePEc:arx:papers:0806.0307
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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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