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Approximating equity volatility

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  • Ahmed Loulit

Abstract

The volatility estimation is a crucial problem for pricing derivatives. The traditional implied volatility approach induces the undesired smile effect and is therefore inconsistent with the market reality. A second more realistic approach is due to Bensoussan, Crouhy and Galai (1995) who derive an extension of the Black-Scholes model where the stochastic volatility ?is endogenous and depends on the change in the firm’s financial leverage. These authors give an analytic approximation for ?when the firm is financed by external funds such as debts, under the assumptions that the risk-free rate and the volatility of the return on the firm’s asset are constant. In this work, we will generalize this result by allowing these parameters to be variable.

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Paper provided by ULB -- Universite Libre de Bruxelles in its series Working Papers CEB with number 04-028.RS.

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Length: 18 p.
Date of creation: 2004
Date of revision:
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Handle: RePEc:sol:wpaper:04-028

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Keywords: Black-Scholes model; derivative pricing; volatility.;

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  1. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  2. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-51.
  3. Jackwerth, Jens Carsten, 1996. "Generalized Binomial Trees," MPRA Paper 11635, University Library of Munich, Germany, revised 12 May 1997.
  4. 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.
  5. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-67, May.
  6. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers, University of California at Berkeley RPF-232, University of California at Berkeley.
  7. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
  8. 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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