广西师范大学学报（自然科学版） ›› 2021, Vol. 39 ›› Issue (5): 158-172.doi: 10.16088/j.issn.1001-6600.2020121101

• 研究论文 • 上一篇    下一篇

随机利率跳扩散模型下幂型乘积远期生效期权定价

谢冬林, 邓国和*   

  1. 广西师范大学 数学与统计学院, 广西 桂林 541006
  • 收稿日期:2020-12-11 修回日期:2021-03-06 出版日期:2021-09-25 发布日期:2021-10-19
  • 通讯作者: 邓国和(1969—), 男, 湖南桂阳人, 广西师范大学教授, 博导。E-mail: dengguohe@gxnu.edu.cn
  • 基金资助:
    国家自然科学基金(11461008); 广西自然科学基金(2018GXNSFAA281016)

Pricing Forward-start Power Options with Product of Two Assets in a Stochastic Interest Rate and Jump Diffusion Model

XIE Donglin, DENG Guohe*   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2020-12-11 Revised:2021-03-06 Online:2021-09-25 Published:2021-10-19

PDF (PC)

384

摘要： 在随机利率下考虑标的资产价格服从跳扩散过程的两资产幂型乘积远期生效期权的定价。应用Feynman-Kac定理、联合特征函数及Fourier反变换等方法获得了两资产欧式幂型乘积远期生效期权价格的显示解。应用离散快速Fourier变换(FFT)对期权价格进行数值计算, 并应用Monte Carlo模拟法检验了FFT方法的有效性。应用本文方法比较4类市场模型下期权价格的变化情况, 分析幂型乘积远期生效期权价格依赖于标的资产价格的跳跃风险因素、期权生效日与到期日、两资产价格间相关系数、利率的均值回复速度和长期均值水平等主要参数的敏感性。数值结果表明:跳跃风险因素、期权生效日与到期日、相关系数和利率的长期均值水平对期权价格具有较为显著影响, 利率的均值回复速度对期权价格也有一定的作用, 这些结果有利于投资者进行风险管理与对冲。

关键词: 幂期权, 乘积期权, 远期生效期权, CIR随机利率, Girsanov定理, Fourier反变换

Abstract: In this paper, the pricing problem on forward-start power options with product of two assets followed jump diffusion models in a stochastic interest rate framework is considered. Using the Feynman-Kac theorem, the joint characteristic function and the Fourier inverse transformation techniques, the closed-explicit solutions of the European forward-start power options with product of two asset are obtained. Some numerical examples for the option price are implemented by the fast Fourier transform (FFT), and the validity of the proposed method is verified by Monte Carlo simulation. The changes of option price in the proposed model were compared with that of other three different models (Black-Scholes, Merton and CIR+Black-Scholes), and the sensitivity of the price of the forward-start power options with product of two assets to some main parameters were analyzed, including the power factor, jump risk factors, maturity date, the correlation coefficient, average recovery speed and long term average level of interest rate, in the proposed model. Numerical results show that the power factor, jump risk factors, maturity date, the correlation coefficient, and long term average level of interest rate have more significant effect on the option price, and average recovery speed of interest rate has some effects on the option price. These are beneficial to risk management and hedging for investors.

Key words: power option, product option, forward-start option, CIR stochastic interest rate model, Girsanov theorem, Fourier inverse transformation

中图分类号: 

  • O212.1
[1] MERTON R C. Option pricing when underlying stock return are discontinuous[J]. Journal of Financial Economics, 1976, 3(1/2): 125-144.
[2] COX J C, INGERSOLL J E, ROSS S A. A theory of the term structure of interest rates[J]. Econometrica, 1985, 53(2): 385-407.
[3] BLACK F, SCHOLES M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81(3): 637-654.
[4] HEYNEN R C, KAT H M. Pricing and hedging power options[J]. Financial Engineering and the Japanese Markets, 1996, 3(3): 253-261.
[5] WILIMOTT P. Derivatives: the theory and practice of financial engineering[M]. New York: John Wiley & Sons, 2000: 121-122, 235-237.
[6] ZHANG P G. Exotic options[M]. 2nd ed. 北京: 世界图书出版公司, 2009:187-193, 439-446.
[7] 郭培栋, 张寄洲. 双币种博弈期权[J]. 数学的实践与认识, 2017, 47(24): 21-29.
[8] RUBINSTEIN M. Pay now, choose later[J]. Risk, 1991, 4(2): 44-47.
[9] 杨向群, 吴奕东. 带跳的幂型支付欧式期权定价[J]. 广西师范大学学报(自然科学版), 2007, 25(3): 56-59.
[10] 苏小囡, 王文胜. 幂式期权在跳扩散模型下的定价[J]. 华东师范大学学报(自然科学版), 2011(3): 12-20, 53.
[11] 刘佳钥. 乘积期权的定价及应用[D]. 石家庄: 河北师范大学, 2018.
[12] 杨建奇, 赵守娟. 双指数跳扩散模型下远期生效期权的定价[J]. 数学的实践与认识, 2017, 47(6): 29-34.
[13] 林涵彬, 苏小囡, 王伟. 混合指数跳扩散模型下远期生效期权的定价[J]. 宁波大学学报(理工版), 2019, 32(5): 104-109.
[14] HUANG J, ZHU W, RUAN X. Fast Fouriertransform based power option pricing with stochastic interest rate, volatility, and jump intensity[J]. Journal of Applied Mathematics, 2013: 875606.
[15] 韦铸娥, 奚欢, 何家文. 随机波动率与跳扩散组合模型的双币种期权定价[J]. 数学的实践与认识, 2019, 49(11): 306-312.
[16] KRUSE S, NOGEL U. On the pricing of forward starting options in Heston's model on stochastic volatility[J]. Finance and Stochastics, 2005, 9(2): 233-250.
[17] AHLIP R, RUTKOWSKI M. Forward start options under stochastic volatility and stochastic interest rates[J]. International Journal of Theoretical and Applied Finance, 2009, 12(2): 209-225.
[18] 黄国安, 邓国和. 随机波动率下跳扩散模型的远期生效期权[J]. 广西师范大学学报(自然科学版), 2009, 27(3): 35-39.
[19] ZHANG S, SUN Y. Forward starting options pricing with double stochastic volatility, stochastic interest rates and double jumps[J]. Journal of Computational and Applied Mathematics,2017, 325: 34-41.
[20] 薛广明, 邓国和. 带跳随机利率与波动率模型的远期生效期权定价[J]. 数学杂志, 2019, 39(3): 414-430.
[21] XUE G M, DENG G H. Pricing forward-starting power Asian options with floating strike price[J]. Mathematica Applicate, 2017, 30(4): 916-926.
[22] LEE J, LEE Y. Pricing symmetric type of power quanto options[J]. Bulletin of the Korean Mathematical Society, 2019, 56(2): 351-364.
[23] 韦铸娥, 何家文. 基于带跳随机波动率模型的双币种重置期权定价研究[J]. 数学的实践与认识, 2020, 50(3): 48-59.
[24] DUFFINE D, PAN J, SINGLETON K. Transform analysis and asset pricing for affine jump-diffusions[J].Econometrica, 2000, 68(6): 1343-1376.
[25] CARR P, MADAN D. Option valuation using the fast Fourier transform[J]. Journal of Computational Finance, 1999, 2(4): 61-73.
[1] 温小梅, 邓国和. 双随机波动率跳扩散模型的复合幂期权定价[J]. 广西师范大学学报（自然科学版）, 2021, 39(2): 101-111.
[2] 邓国和. Heston模型的欧式任选期权定价与对冲策略[J]. 广西师范大学学报（自然科学版）, 2012, 30(3): 36-43.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 黄李, 邹艳丽, 王意, 李可. 分布式电站的3种入网方式比较研究[J]. 广西师范大学学报（自然科学版）, 2017, 35(3): 30 -36 .
[2] 苏旭, 刘玉萍. 青海省药用植物野薄荷光合特性的研究[J]. 广西师范大学学报（自然科学版）, 2011, 29(2): 76 -81 .
[3] 卢其西, 林勇, 宾石玉, 唐章生, 彭婷. 罗非鱼6个家系的低温耐寒测定分析[J]. 广西师范大学学报（自然科学版）, 2011, 29(2): 104 -109 .
[4] 唐楠, 杨志豪, 吴佳金, 王艳华, 林鸿飞. 基于监督学习的蛋白质络合物抽取方法[J]. 广西师范大学学报（自然科学版）, 2011, 29(2): 174 -179 .
[5] 刘杰, 张姿, 黄廷磊. 移动AODV路由协议的设计与性能评估[J]. 广西师范大学学报（自然科学版）, 2013, 31(2): 39 -44 .
[6] 尤利华, 黄荣辉. Fibonacci数的标准分解式中诸奇素因数的指数[J]. 广西师范大学学报（自然科学版）, 2011, 29(3): 18 -22 .
[7] 黄廷洪, 王苗, 马凯, 杨坤国, 黄瑛达, 游腾丽, 王修建. [Ag(pba)(Et-dtc)]·p-C6H4(CH3)2配合物的合成、晶体结构及光谱性质[J]. 广西师范大学学报（自然科学版）, 2011, 29(3): 43 -46 .
[8] 马盈仓, 张美, 崔美英. Frank三角范数的三值模糊逻辑系统的真度理论[J]. 广西师范大学学报（自然科学版）, 2011, 29(3): 84 -88 .
[9] 沈泽豪, 叶中行. 期货公司客户风险管理的模糊聚类分析[J]. 广西师范大学学报（自然科学版）, 2011, 29(3): 101 -104 .
[10] 陈尤莺, 郑之, 孔祥增, 张胜元. 基于贝叶斯分类器的结肠癌数据分类[J]. 广西师范大学学报（自然科学版）, 2011, 29(3): 187 -191 .
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发