广西师范大学学报（哲学社会科学版） ›› 2021, Vol. 39 ›› Issue (2): 101-111.doi: 10.16088/j.issn.1001-6600.2019100301

• CCIR2020 • 上一篇    下一篇

双随机波动率跳扩散模型的复合幂期权定价

温小梅, 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:2019-10-03 修回日期:2019-12-15 出版日期:2021-03-25 发布日期:2021-04-15
  • 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@mailbox.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)

Valuation on Compound Power Options under Double StochasticVolatility Jump Diffusion Model

WEN Xiaomei, DENG Guohe*   

  1. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2019-10-03 Revised:2019-12-15 Online:2021-03-25 Published:2021-04-15

摘要： 基于股价满足双随机波动率跳扩散模型的市场模型,考察复合幂期权定价问题。利用多维随机向量的特征函数、偏微分-积分方程、Fourier反变换等方法,得到欧式复合幂期权价格的解析表达式;应用数值计算实例分析不同市场模型下复合幂期权的价格比较,考查该市场模型中主要参数对期权价格的影响。计算结果表明:股价的波动率和跳跃强度因素对期权价格产生较大效果;复合幂期权有较好的风险管理灵活性, 也能给投资者带来更大收益。

关键词: 幂期权, 复合期权, 双Heston随机波动率模型, 跳扩散模型

Abstract: The pricing of the European compound power options is considered under double stochastic volatility jump diffusion model. By using multivariate characteristic function, partial differential-integral equation and the Fourier inversion transform, the analytic formulas for the European compound power options are obtained. Comparison on prices of this option under some differential models is discussed and impact of the main parameters for the proposed model on option price is investigated with some numerical examples. Numerical results show that both the stock’s volatility and the jump intensity can produce considerable effect on option price, and the compound power option has not only better risk management flexibility but also greater returns to investors.

Key words: power option, compound option, double Heston stochastic volatility model, jump diffusion model.

中图分类号: 

  • O211.9
[1] GESKE R.The valuation of compound options[J].Journal of Financial Economics,1979,7(1):63-81.DOI: 10.1016/0304-405X(79)90022-9.
[2]SELBY M J P,HODGES S D.On the evaluation of compound options[J].Management Science,1987,33(3):347-355.
[3]BURASCHI A,DUMAS B.The forward valuations of compound option[J].Journal of Derivatives,2001,9(1):8-17.DOI: 10.3905/jod.2001.319165.
[4]李荣华,戴永红,常秦.参数依赖于时间的复合期权[J].工程数学学报,2005,25(4):692-696.
[5]GUKHAL C R.The compound option approach to American options on jump-diffusions[J].Journal of Economic Dynamics and Control,2004,28(10):2055-2074.DOI: 10.1016/j.jedc.2003.06.002.
[6]LIU Y H,JIANG I M,HSUA W T.Compound option pricing under a double exponential jump diffusion model[J].North American Journal of Economics and Finance,2018,43:30-53.DOI: 10.1016/j.najef.2017.10.002.
[7]GRIEBSCH S A.The evaluation of European compound option prices under stochastic volatility using Fourier transform techniques[J].Review of Derivatives Research,2013,16(2):135-165.DOI: 10.1007/s11147-012-9083-z.
[8]CHIARELLA C,GRIEBSCH S,KANG B.A comparative study on time-efficient methods to price compound options in the Heston model[J].Computers and Mathematics with Applications,2014,67(6):1254-1270.DOI:10.1016/j.camwa.2014.01.008.
[9]FOUQUE J P,HAN C H.Evaluation of compound options using perturbation approximation[J].Journal of Computational Finance,2005,9(1):41-61.DOI: 10.21314/JCF.2005.125.
[10]SCOTT L O.Pricing stock options in a jump-diffusion model with stochastic volatility and interest rates:applications of Fourier inversion methods[J].Mathematical Finance,1997,7(4):413-426.DOI: 10.1111/1467-9965.00039.
[11]DUFFIE D,PAN J,SINGLETON K J.Transform analysis and asset pricing for affine jump-diffusions[J].Econometrica,2000,68(6):1343-1376.
[12]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.
[13]邓国和.随机波动率跳跃扩散模型下复合期权定价[J].数理统计与管理,2015,34(5):910-922.
[14]苏甜.双因素随机波动率跳扩散模型下复合期权定价[D].桂林:广西师范大学,2017.
[15]HEYNEN R C,KAT H M.Pricing and hedging power options[J].Financial Engineering and the Japanese Markets,1996,3(3):253-261.DOI: 10.1007/BF02425804.
[16]TOMPKINS R G.Power options:hedging nonlinear risks[J].Journal of Risk,2000,2(2):29-45.DOI: 10.21314/JOR.2000.022.
[17]MACOVSCHI S,QUITTARD-PINON F.On the pricing of power and other polynomial options[J].The Journal of Derivatives,2006,13(4):61-71.DOI: 10.3905/jod.2006.635421.
[18]ESSER A.General valuation principles for arbitrary payoffs and applications to power options under stochastic volatility[J].Financial Markets and Portfolio Management,2003,17(3):351-372.DOI: 10.1007/s11408-003-0305-0.
[19]KIM J,KIM B,MOON K S,et al.Valuation of power options under Heston’s stochastic volatility model[J].Journal of Economic Dynamics and Control,2012,36(11):1796-1813.DOI: 10.1016/j.jedc.2012.05.005.
[20]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.
[21]符双,薛红.分数跳-扩散O-U过程下幂型期权定价[J].哈尔滨商业大学学报(自然科学版),2014,30(6):758-762.
[22]XUE G M,DENG G H.Pricing forward-starting power asian options with floating strike price[J].Mathematica Applicata,2017,30(4):916-926.
[23]CHERNOV M,RONALD GALLLANT A,GHYSELS E,et al.Alternative models for stock price dynamics[J].Journal of Econometrics,2003,116(1/2):225-257.DOI:10.1016/S0304-4076(03)00108-8.
[24]CARRP,WU L.Stochastic skew in currency options[J].Journal of Financial Economics,2007,86(1):213-247.
[25]FONSECA J D,GRASSELLI M,TEBALDI C.A multi-factor volatility Heston model[J].Quantitative Finance,2008,8(6):591-604.DOI: 10.1080/14697680701668418.
[26]ERAKER B,JOHANNES M,POLSON N.The impact of jumps in volatility and returns[J].The Journal of Finance,2003,58(3):1269-1300.DOI: 10.1111/1540-6261.00566.
[27]AHLIP R,PARK L A F,PRODAN A.Semi-analytical option pricing under double Heston jump-diffusion hybrid model[J].Journal of Mathematical Sciences and Modelling,2018,1(3):138-152.DOI: 10.33187/jmsm.432019.
[28]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.DOI: 10.1080/00949655.2015.1046072.
[29]邓国和.双跳跃仿射扩散模型的美式看跌期权定价[J].系统科学与数学,2017,37(7):1646-1663.
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