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Two unconditionally implied parameters and volatility smiles and skews

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  • Nikolai Dokuchaev

Abstract

The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the risk-free interest rate. In reality, the risk free interest rate is unknown and need to be forecasted, because the option price depends on its future curve. Therefore, the standard implied volatility is {\it conditional}: it depends on the future values of the risk free rate. We study two implied parameters: the implied volatility and the implied average cumulative risk free interest rate. They can be found unconditionally from a system of two equations. We found that very simple models with random volatilities (for instance, with two point distributions) generate various volatility smiles and skews with this approach.

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File URL: http://arxiv.org/pdf/1303.4847
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Paper provided by arXiv.org in its series Papers with number 1303.4847.

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Date of creation: Mar 2013
Date of revision: Apr 2013
Publication status: Published in Applied Financial Economics Letters 2006, V. 2, 199-204
Handle: RePEc:arx:papers:1303.4847

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  1. Rheinländer, Thorsten & Schweizer, Martin, 1997. "On L2-projections on a space of stochastic integrals," SFB 373 Discussion Papers 1997,25, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, American Finance Association, vol. 27(2), pages 399-417, May.
  3. 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.
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