Black-Scholes Option Pricing Model Modified to Admit a Miniscule Drift Can Reproduce the Volatility Smile

Show more

References

[1] B. Dupire, “Pricing with a Smile,” Risk, Vol. 7, No. 1, 1994, pp. 18-20.

[2] F. Black and M. S. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-654. doi:10.1086/260062

[3] R. Merton, “Option Pricing When Underlying Stock Returns Are Discontinuous,” Journal of Financial Economics, Vol. 3, No. 1-2, 1976, pp. 125-144.
doi:10.1016/0304-405X(76)90022-2

[4] F. Black, “The Pricing of Commodity Contracts,” Journal of Financial Economics, Vol. 3, 1976, pp. 167-179.
doi:10.1016/0304-405X(76)90024-6

[5] J.-P. Bouchaud and M. Potters, “Back to Basics: Historical Option Pricing Revisited,” Philosophical Transactions of the Royal Society, Vol. 357, No. 1735, 1999, pp. 2019-2028.

[6] E. Derman, “Regimes of Volatility,” Risk, Vol. 4, 1999, pp. 55-59.

[7] E. Derman and I. Kani, “Riding on a Smile,” Risk, Vol. 7, No. 2, 1994, pp. 32-39.

[8] M. Rubinstein, “Implied Binomial Trees,” Journal of Finance, Vol. 49, No. 3, 1994, pp. 771-818.

[9] L. Andersen and R. Brotherton-Ratcliffe, “The Equity Option Volatility Smile: An Implicit Finite-Difference Approach,” Journal of Computational Finance, Vol. 1, No. 2, 1997, pp. 5-38.

[10] J. C. Hull and A. White, “An Analysis of the Bias in Option Pricing Caused by a Stochastic Volatility,” Advances in Futures and Options Research, Vol. 3, 1988, pp. 29-61.

[11] S. L. Heston, “A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options,” Review of Financial Studies, Vol. 6, No. 2, 1993, pp. 327-343. doi:10.1093/rfs/6.2.327

[12] D. S. Bates, “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options,” Review of Financial Studies, Vol. 9, No. 1, 1996, pp. 69107. doi:10.1093/rfs/9.1.69

[13] B. Dupire, “A Unified Theory of Volatility,” Working Paper, 1996.

[14] A. Lipton and W. McGhee, “Universal Barriers,” Risk, Vol. 15, No. 5, 2002, pp. 81-85.

[15] M. Britten-Jones and A. Neuberger, “Option Prices, Implied Prices Processes, and Stochastic Volatility,” Journal of Finance, Vol. 55, No. 2, 2000, pp. 839-866.
doi:10.1111/0022-1082.00228

[16] G. Blacher, “A New Approach for Designing and Calibrating Stochastic Volatility Models for Optimal DeltaVega Hedging of Exotic Options,” Conference presentation at Global Derivatives and Risk Management, Juanles-Pins, 26 June 2002.

[17] D. Brigo and F. Mercurio, “A Mixed-Up Smile,” Risk, Vol. 13, No. 9, 2000, pp. 123-126.

[18] R. Hillborn and M. Mangel, “The Ecological Detective: Confronting Models with Data,” Princeton University Press, Princeton, 1997

[19] R. L. McDonald, “Derivative Markets,” 2nd Edition, Addison Wesley, New York, 2006.