# 分数布朗运动环境下的资产配置策略多期收益保证价值的测算Pricing Multi-Period Return Guarantees Combined with Asset Allocation Strategy under Fractional Brownian Motion

DOI: 10.12677/FIN.2016.62007, PDF, HTML, XML, 下载: 1,677  浏览: 5,516  国家自然科学基金支持

Abstract: In this paper, we consider that the price processes of risky assets are driven by fractional Brownian motion (1/2< H< 1). With the Wick-Itô integral and the quasi-conditional expectation, we compute the value of multi-period return guarantees under CM strategy and under CPPI strategy. Through the numerical simulation, the influence on the value of multi-period return guarantees under the two strategies is compared and analyzed, which is made by the periods of multi-period return guarantees and the important parameters of the financial market and asset allocation strategy.

 [1] Brennan, J.M. and Schwartz, E.S. (1976) The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee. Journal of Financial Economics, 3, 195-213. http://dx.doi.org/10.1016/0304-405X(76)90003-9 [2] 张飞, 刘海龙. 价格跳跃风险下CPPI策略多期收益保证价值的测算[J]. 系统工程理论与实践, 2014, 34(8): 1944- 1951. [3] 王亦奇, 刘海龙. 结合资产配置策略测算多期收益保证价值[J]. 管理科学学报, 2011, 14(11): 42-51. [4] Black, F. and Scholes, M. (1973) The Pricing of Options and Gorporate Liabilities. Journal of Political Economy, 81, 637-654. http://dx.doi.org/10.1086/260062 [5] Shiryaev, A.N. (1999) Essentials of Stochastic Finance. World Scientific, Singapore. [6] Rogers, L. (1997) Arbitrage with Fractional Brownian Motion. Mathematical Finance, 7, 95-105. http://dx.doi.org/10.1111/1467-9965.00025 [7] Bjork, T. and Hult, H. (2005) A Note on Wick Products and the Fractional Black-Scholes Model. Finance and Stochastics, 9, 197-209. http://dx.doi.org/10.1007/s00780-004-0144-5 [8] Sottinen, T. (2001) Fractional Brownian Motion, Random Walks and Binary Market Models. Finance and Stochastics, 5, 343-355. http://dx.doi.org/10.1007/PL00013536 [9] Necula, C. (2002) Option Pricing in a Fractional Brownian Motion Environment. Work Papers. http://dx.doi.org/10.2139/ssrn.1286833 [10] Hu, Y. and Oksendal, B. (2003) Fractional White Noise Calculus and Applications to Finance. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 6, 1-32. http://dx.doi.org/10.1142/S0219025703001110 [11] Biagini, F. and Hu, Y., Øksendal, B. and Zhang, T. (2008) Stochastic Calculus for Fractional Brownian Motion and Applications. Springer, Berlin. [12] Rostek, S. and Schobel, R. (2006) Risk Preference Based Option Pricing in a Fractional Brownian Market. Tubinger Diskussinsbeitrag, Tu-ebingen.