A Simple Method to Price Window Reset Options
Author(s)
Yi-Long Hsiao
ABSTRACT
A window reset option is a kind of reset options with continuous reset constraints. The issue is very important for applying to employee stock options in finance or reservation options on truck-only toll lanes in traffic management. Our contribution of this study is that we proposed an accurate and simple method to price window reset options. The option price is formulated as the solution of a boundary value problem of the Black-Scholes PDE. The problem is then transformed into an initial-boundary value problem of the heat equation. Then Green’s function is applied to solve the heat equation problem. Finally, the option price is calculated numerically. A numerical example and some discussions are presented in this paper.
Cite this paper
Y. Hsiao, "A Simple Method to Price Window Reset Options," Journal of Mathematical Finance, Vol. 3 No. 1, 2013, pp. 96-102. doi: 10.4236/jmf.2013.31008.
Y. Hsiao, "A Simple Method to Price Window Reset Options," Journal of Mathematical Finance, Vol. 3 No. 1, 2013, pp. 96-102. doi: 10.4236/jmf.2013.31008.
References
[1] W. Cheng and S. Zhang, “The Analytics of Reset Options,” Journal of Derivatives, Vol. 8, No. 1, 2000, pp. 59-71. doi:10.3905/jod.2000.319114 [2] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” The Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-654. doi:10.1086/260062 [3] R. C. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, Vol. 4, No. 1, 1973, pp. 141-183. doi:10.2307/3003143 [4] S. Gray and R. Whaley, “Valuing S&P 500 Bear Market Reset Warrants with A Periodic Reset,” Journal of Derivatives, Vol. 5, No. 1, 1997, pp. 99-106. doi:10.3905/jod.1997.407987 [5] S. Gray and R. Whaley, “Reset Put Options: Valuation, Risk Characteristics, and An Application,” Australian Journal of Management, Vol. 24, No. 1, 1999, pp. 1-20. doi:10.1177/031289629902400101 [6] S.-L. Liao and C.-W. Wang, “The Valuation of Reset Options with Multiple Strike Resets and Reset Dates,” The Journal of Futures and Markets, Vol. 23, No. 1, 2003, pp. 87-107. doi:10.1002/fut.10055 [7] T. S. Dai, Y. Y. Fang and Y. D. Lyuu, “Analytics for Geo- metric Average Trigger Reset Options,” Applied Economics Letters, Vol. 12, No. 13, 2005, pp. 835-840. doi:10.1080/1350485052000345500 [8] Y. L. Hsiao, A. M. L. Wang and C. Y. Chen, “Pricing an Arithmetic Average Reset Option Using the Green Function Method,” Asia Pacific Management Review, 2011. [9] S. Y. Shen and A. M. L. Wang, “On Stop-Loss Strategies for Stock Investments,” Applied Mathematics and Computation, Vol. 119, No. 2-3, 2001, pp. 317-337. doi:10.1016/S0096-3003(99)00229-5 [10] Y.-L. Hsiao, “Closed-Form Approximate Solutions of Window Barrier Options with Term-Structure Volatility and Interest Rates Using the Boundary Integral Method,” Journal of Mathematical Finance, Vol. 2, No. 4, 2012, pp. 291-302. doi:10.4236/jmf.2012.24032 [11] D. Kincaid and W. Chency, “Numerical Analysis,” Brooks/ Code Publishing Company, Pacific Grove, 1991, p. 460.
[1] W. Cheng and S. Zhang, “The Analytics of Reset Options,” Journal of Derivatives, Vol. 8, No. 1, 2000, pp. 59-71. doi:10.3905/jod.2000.319114 [2] F. Black and M. Scholes, “The Pricing of Options and Corporate Liabilities,” The Journal of Political Economy, Vol. 81, No. 3, 1973, pp. 637-654. doi:10.1086/260062 [3] R. C. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, Vol. 4, No. 1, 1973, pp. 141-183. doi:10.2307/3003143 [4] S. Gray and R. Whaley, “Valuing S&P 500 Bear Market Reset Warrants with A Periodic Reset,” Journal of Derivatives, Vol. 5, No. 1, 1997, pp. 99-106. doi:10.3905/jod.1997.407987 [5] S. Gray and R. Whaley, “Reset Put Options: Valuation, Risk Characteristics, and An Application,” Australian Journal of Management, Vol. 24, No. 1, 1999, pp. 1-20. doi:10.1177/031289629902400101 [6] S.-L. Liao and C.-W. Wang, “The Valuation of Reset Options with Multiple Strike Resets and Reset Dates,” The Journal of Futures and Markets, Vol. 23, No. 1, 2003, pp. 87-107. doi:10.1002/fut.10055 [7] T. S. Dai, Y. Y. Fang and Y. D. Lyuu, “Analytics for Geo- metric Average Trigger Reset Options,” Applied Economics Letters, Vol. 12, No. 13, 2005, pp. 835-840. doi:10.1080/1350485052000345500 [8] Y. L. Hsiao, A. M. L. Wang and C. Y. Chen, “Pricing an Arithmetic Average Reset Option Using the Green Function Method,” Asia Pacific Management Review, 2011. [9] S. Y. Shen and A. M. L. Wang, “On Stop-Loss Strategies for Stock Investments,” Applied Mathematics and Computation, Vol. 119, No. 2-3, 2001, pp. 317-337. doi:10.1016/S0096-3003(99)00229-5 [10] Y.-L. Hsiao, “Closed-Form Approximate Solutions of Window Barrier Options with Term-Structure Volatility and Interest Rates Using the Boundary Integral Method,” Journal of Mathematical Finance, Vol. 2, No. 4, 2012, pp. 291-302. doi:10.4236/jmf.2012.24032 [11] D. Kincaid and W. Chency, “Numerical Analysis,” Brooks/ Code Publishing Company, Pacific Grove, 1991, p. 460.