混合分数跳-扩散模型下的亚式期权定价

doi:10.3969/j.issn.1000-5641.2017.03.003

华东师范大学学报(自然科学版) ›› 2017, Vol. ›› Issue (3): 29-38.doi: 10.3969/j.issn.1000-5641.2017.03.003

混合分数跳-扩散模型下的亚式期权定价

耿延静, 周圣武

中国矿业大学数学系, 江苏徐州 221008

收稿日期:2016-06-23 出版日期:2017-05-25 发布日期:2017-05-18
通讯作者: 周圣武,男,教授,研究方向为金融数学.E-mail:zswcumt@163.com E-mail:zswcumt@163.com
作者简介:耿延静,女,硕士研究生,研究方向为金融数学.E-mail:gengyanjing_ah@qq.com
基金资助:
中央高校基本科研业务费专项资金（2013XK03）

Pricing Asian option under mixed jump-fraction process

GENG Yan-jing, ZHOU Sheng-wu

Department of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221008, China

Received:2016-06-23 Online:2017-05-25 Published:2017-05-18

摘要/Abstract

摘要： 给出了标的资产服从混合分数跳-扩散过程的几何平均亚式期权定价的解析解.运用广义Itô引理和自融资交易策略得到混合分数布朗运动下带跳的几何平均亚式期权定价的偏微分方程模型.结合边值条件，通过求解该偏微分方程得到亚式期权定价的解析解.通过数值试验，讨论各定价参数对期权价值的影响.本文推广了一些已有的结论，所得结果更贴近实际金融市场.

关键词: 混合分数跳-扩散过程, 几何平均亚式期权, 偏微分方程

Abstract: This paper mainly studied the geometric average Asian option pricing on the condition that the underlying asset followed mixed jump-fraction process. The general Itô's lemma and the self-financing dynamic strategy were obtained by using the partial differential equation of such option pricing in the mixed fractional environment with jump. With the combination of boundary condition, an analytic formula for the geometric average Asian option was derived by solving the partial differential equation. The numerical experiments were showed to discuss the influence of different parameters on the option value. The results were the generalization of some existing results which was closer to the real financial market.

Key words: mixed jump-fraction process, geometric average Asian option, partial differential equation

中图分类号:

O211.6

耿延静, 周圣武. 混合分数跳-扩散模型下的亚式期权定价[J]. 华东师范大学学报(自然科学版), 2017, (3): 29-38.

GENG Yan-jing, ZHOU Sheng-wu. Pricing Asian option under mixed jump-fraction process[J]. Journal of East China Normal University(Natural Sc, 2017, (3): 29-38.

参考文献

[1] KEMNA A G Z, VORST A C F. A pricing method for options based on average asset values [J]. Journal of Banking and Finance, 1990, 14(1): 113-129.
[2] WONG H Y, CHEUNG H L. Geometric Asian options: Valuation and calibration with stochastic volatility [J]. Quantitative Finance, 2004, 4(3): 301-314.
[3] CHOU C S, LIN H J. Asian options with jumps [J]. Statistics & Probability, 2006, 6(14): 1983-1993.
[4] CHERIDITO P. Regularizing fractional Brownian motion with a view towards stock price modelling [D]. Zürich: Swiss Federal Institute of Technology, 2001.
[5] CHERIDITO P. Arbirage in fractional Brownian motion models [J]. Finance and Stochastics, 2003, 7(4): 533-553.
[6] KUZNETSOV Y A. The absence of arbitrage in a model with fractal Brownian motion [J]. Russian Mathematical Surveys, 1999, 54(4): 847-848.
[7] ZÄHLE M. Long range dependence, no arbitrage and the Black–Scholes formula [J]. Stochastics and Dynamics, 2002, 2(2): 265-280.
[8] MISHURA Y S. Stochastic Calculus for Fractional Brownian Motion and Related Processes [M]. Berlin: Springer, 2008.
[9] WANG X T. Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model [J]. Physica A, 2010, 389(3): 438-444.
[10] WANG X T. Scaling and long-range dependence in option pricing V: Multiscaling hedging and implied volatility smiles under the fractional Black–Scholes model with transaction costs [J]. Physica A, 2011, 390(9): 1623-1634.
[11] MEHRDOUST F, SABER N. Pricing arithmetic Asian option under a two-factor stochastic volatility model with jumps [J]. Journal of Statistical Computation and Simulation, 2015, 85(18): 3811-3819.
[12] RAMBEERICH N. A high order finite element scheme for pricing options under regime switching jump diffusion processes [J]. Journal of Computational and Applied Mathematics, 2016, 300(2): 83-96.
[13] XIAO W L. Pricing currency options in a fractional Brownian motion with jumps[J]. Economic Modelling, 2010, 27(5): 935-942.
[14] PENG B. Pricing Asian power options under jump-fraction process [J]. Journal of Economics, Finance and Administrative Science, 2012, 17(33): 2-9.
[15] 丰月姣. 带跳混合分数布朗运动下利差期权定价[J]. 佳木斯大学学报,(自然科学版), 2013, 30(6): 922-925.
[16] 孙玉东. 带跳混合分数布朗运动下利差期权定价[J]. 系统科学与数学, 2013, 32(11): 1377-1385.
[17] SHOKROLLAHI F. Actuarial approach in a mixed fractional Brownian motion with jumps environment for pricing currency option [J]. Advances in Difference Equations, 2015, 257(1): 1-8.

混合分数跳-扩散模型下的亚式期权定价

Pricing Asian option under mixed jump-fraction process

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价

[1]	林文贤. 带脉冲的多时滞分数阶阻尼偏微分方程解的强迫振动性[J]. 华东师范大学学报（自然科学版）, 2024, 2024(2): 33-41.
[2]	代慧菊, 李连忠, 王琪, 沙安. 一类四阶偏微分方程的李对称分析、Bäcklund变换及其精确解[J]. 华东师范大学学报(自然科学版), 2019, 2019(1): 24-31.
[3]	马飞, 姚兵. 基于两种不同择优概率下的无标度网络模型[J]. 华东师范大学学报(自然科学版), 2017, 2017(6): 42-49.
[4]	蔡江涛. 一类二阶向量中立型阻尼偏微分方程的H-振动性[J]. 华东师范大学学报(自然科学版), 2011, 2011(5): 73-78.