定时器期权定价的Fourier-Cosine方法
A Fourier-Cosine Method for Pricing Timer Options
DOI: 10.12677/PM.2016.65061, PDF, HTML, XML, 下载: 1,687  浏览: 3,248  国家自然科学基金支持
作者: 徐艳妍, 曾有栋:福州大学,福建 福州
关键词: Heston模型定时器期权Fourier-Cosine方法Heston Model Timer Options Fourier-Cosine Method
摘要: 定时器期权是有着不确定到期日的障碍类型期权。根据标的资产的累计实现方差达到预指定的水平就强制执行的特性,在随机波动模型(Heston model)下,提出Fourier-cosine方法定价有限到期日定时器期权,得到定价表达式。数值结果说明该方法的精确性。
Abstract: Timer options have an uncertain expiration date of barrier style options. The finite-maturity timer option expires when the accumulated realized variance of the underlying asset has reached a pre-specified level. We construct the Fourier-cosine method for pricing discrete timer options under Heston model. Numerical results illustrate the accuracy of the Fourier-cosine method.
文章引用:徐艳妍, 曾有栋. 定时器期权定价的Fourier-Cosine方法[J]. 理论数学, 2016, 6(5): 449-458. http://dx.doi.org/10.12677/PM.2016.65061

参考文献

[1] Bick, A. (1995) Quadratic-Variation-Based Dynamic Strategies. Management Science, 41, 722-732. http://dx.doi.org/10.1287/mnsc.41.4.722
[2] Li, C. (2016) Bessel Processes, Stochastic Volatility, and Timer Options. Mathematical Finance, 26, 122-148. http://dx.doi.org/10.1111/mafi.12041
[3] Bernard, C. and Cui, Z.Y. (2011) Pricing Timer Options. Journal of Computational Finance, 15, 69-104. http://dx.doi.org/10.21314/JCF.2011.228
[4] Liang, L.Z.J., Lemmens, D. and Tempere, J. (2011) Path Integral Approach to the Pricing of Timer Options with the Duru-Kleinert Time Transformation. Physical Review E, 83, 1-12. http://dx.doi.org/10.1103/PhysRevE.83.056112
[5] Saunders, D. (2009) Pricing Timer Options under Fast Mean-Reverting Stochastic Volatility. Canadian Applied Mathematics Quarterly, 17, 737-753.
[6] Li, M. and Mercurio, F. (2014) Closed-Form Approximation of Perpetual Timer Option Prices. International Journal of Theoretical and Applied Finance, 17, Article ID: 1450026. http://dx.doi.org/10.1142/S0219024914500265
[7] Li, M. and Mercurio, F. (2015) Analytic Approximation of Finite-Maturity Timer Option Prices. Journal of Futures Markets, 35, 245-273. http://dx.doi.org/10.1002/fut.21659
[8] Fang, F. and Oosterlee, C.W. (2008) A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions. SIAM Journal on Scientific Computing, 31, 826-848. http://dx.doi.org/10.1137/080718061
[9] Fang, F. and Oosterlee, C.W. (2011) A Fourier-Based Valuation Method for Bermudan and Barrier Options under Heston’s Model. SIAM Journal on Financial Mathematics, 2, 439-463. http://dx.doi.org/10.1137/100794158
[10] Fang, F. and Oosterlee, C.W. (2009) Pricing Early-Exercise and Discrete Barrier Options by Fourier-Cosine Series Expansions. Numerische Mathematik, 114, 27-62. http://dx.doi.org/10.1007/s00211-009-0252-4
[11] Scott, L.O. (1996) Simulating a Multi-Factor Term Structure Model over Relatively Long Discrete Time Periods. Proceedings of the IAFE First Annual Computational Finance Conference, Graduate School of Business, Stanford University, Stanford.
[12] Zeng, P., Kwok, Y.K. and Zheng, W. (2015) Fast Hilbert Transform Algorithms for Pricing Discrete Timer Options under Stochastic Volatility Models. International Journal of Theoretical and Applied Finance, 18, 1-25. http://dx.doi.org/10.1142/S0219024915500466