A Skewness-Adjusted Binomial Model for Pricing Futures Options—The Importance of the Mean and Carrying-Cost Parameters

Stafford Johnson, Amit Sen, Brian Balyeat

Department of Economics, Xavier University, Cincinnati, USA.
Department of Finance, Xavier University, Cincinnati, USA.

DOI: 10.4236/jmf.2012.21013                

Abstract

In this paper, we extend the Johnson, Pawlukiwicz, and Mehta [1] skewness-adjusted binomial model to the pricing of futures options and examine in some detail the asymptotic properties of the skewness model as it applies to futures and spot options. The resulting skewness-adjusted futures options model shows that for a large number of subperiods, the price of futures options depends not only on the volatility and mean but also on the risk-free rate, asset-yield, and other carrying-cost parameters when skewness exists.

Keywords

Options Pricing; Black-Scholes; Skewness

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. S. Johnson, J. E. Pawlukiewicz and J. Mehta, “Binomial Option Pricing with Skewed Asset Returns,” Review of Quantitative Finance and Accounting, Vol. 9, No. 1, 1997, pp. 89-101. doi:10.1023/A:1008283011490
[2]	F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-659. doi:10.1086/260062
[3]	R. S. Johnson, R. A. Zuber and J. M. Gandar, “Binomial pricing of Fixed-Income Securities for Increasing and Decreasing Interest Rate Cases,” Applied Financial Economics, Vol. 16, No. 14, 2006, pp. 1029-1046. doi:10.1080/09603100500426473
[4]	R. S. Johnson, R. A. Zuber and J. M. Gandar, “Pricing Stock Options under Expected Increasing and Decreasing Price Cases,” Quarterly Journal of Business and Economics, Vol. 46, No. 4, 2007, pp. 63-90.
[5]	E. M. Stein and J. C. Stein, “Stock Price Distributions with Stochastic Volatility: An Analytical Approach,” Review of Financial Studies, Vol. 4, No. 4, 1991, pp. 727-752. doi:10.1093/rfs/4.4.727
[6]	J. B. Wiggins, “Option Values under Stochastic Volatility: Theory and Empirical Estimates,” Journal of Financial Economics, Vol. 19, No. 2, 1987, pp. 351-372. doi:10.1016/0304-405X(87)90009-2
[7]	S. L. Heston, “A Closed Form Solution for Options and Stochastic Volatility with Applications to Bond and Currency Options,” Review of Financial Studies, Vol. 6, No. 2, 1993, pp. 327-344. doi:10.1093/rfs/6.2.327
[8]	R. Jarrow and A. Rudd, “Ap-proximate Option Valuation for Arbitrary Stochastic Processes,” Journal of Financial Economics, Vol. 10, No. 3, 1982, pp. 347-369. doi:10.1016/0304-405X(82)90007-1
[9]	C. J. Corrado and T. Su, “Skewness and Kurtosis in S&P 500 Index Returns Implied by Option Prices,” The Journal of Financial Research, Vol. 19, No. 2, 1996, pp. 175- 192.
[10]	A. Camara and S. Chung, “Option Pricing for the Transformed-Binomial Class,” The Journal of Futures Markets, 2006, Vol. 26, No. 8, pp. 759-787. doi:10.1002/fut.20218
[11]	J. C. Cox, S. A. Ross, and M. Rubinstein, “Option Pricing: A Simplified Approach,” Journal of Financial Economics, Vol. 7, No. 3, 1979, pp. 229-263. doi:10.1016/0304-405X(79)90015-1
[12]	R. J. Rendleman and B. J. Bartter, “Two-State Option Pri- cing,” Journal of Finance, Vol. 34, No. 5, 1979, pp. 1093- 1110. doi:10.2307/2327237
[13]	F. Black, “The Pricing of Commod-ity Contracts,” Journal of Financial Economics, Vol. 3, No. 1-2, 1976, pp. 167-179. doi:10.1016/0304-405X(76)90024-6