双随机波动率跳扩散模型的复合幂期权定价

doi:10.16088/j.issn.1001-6600.2019100301

Abstract

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.

CLC Number:

O211.9

WEN Xiaomei, DENG Guohe. Valuation on Compound Power Options under Double StochasticVolatility Jump Diffusion Model[J].Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(2): 101-111.

References

[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.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	HU Jinming, WEI Duqu. Research on Generalized Sychronization of Fractional-order PMSM[J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(6): 14 -20 .
[2]	ZHU Yongjian, LUO Jian, QIN Yunbai, QIN Guofeng, TANG Chuliu. A Method for Detecting Metal Surface Defects Based on Photometric Stereo and Series Expansion Methods[J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(6): 21 -31 .
[3]	YANG Liting, LIU Xuecong, FAN Penglai, ZHOU Qihai. Research Progress in Vocal Communication of Nonhuman Primates in China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 1 -9 .
[4]	BIN Shiyu, LIAO Fang, DU Xuesong, XU Yilan, WANG Xin, WU Xia, LIN Yong. Research Progress on Cold Tolerance of Tilapia[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 10 -16 .
[5]	LIU Jing, BIAN Xun. Characteristics of the Orthoptera Mitogenome and Its Application[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 17 -28 .
[6]	LI Xingkang, ZHONG Enzhu, CUI Chunyan, ZHOU Jia, LI Xiaoping, GUAN Zhenhua. Monitoring Singing Behavior of Western Black Crested Gibbon (Nomascus concolor furvogaster)[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 29 -37 .
[7]	HE Xinming, XIA Wancai, BA Sang, LONG Xiaobin, LAI Jiandong, YANG Chan, WANG Fan, LI Dayong. Grooming Strategies of Resident Males with Different Number of Mates in Yunnan Snub-nosed Monkeys (Rhinopithecus bieti)[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 38 -44 .
[8]	FU Wen, REN Baoping, LIN Jianzhong, LUAN Ke, WANG Pengcheng, WANG Bing, LI Dayong, ZHOU Qihai. Jiyuan Taihang Mountain Macaque Population and Conservation Status[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 45 -52 .
[9]	ZHENG Jingjin, LIANG Jipeng, ZHANG Kechu, HUANG Aimian, LU Qian, LI Youbang, HUANG Zhonghao. White-headed Langurs Select Foods Based on Woody Plants' Dominances[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 53 -64 .
[10]	YANG Chan, WAN Yaqiong, HUANG Xiaofu, YUAN Xudong, ZHOU Hongyan, FANG Haocun, LI Dayong, LI Jiaqi. Activity Rhythm of Muntiacus reevesi Based on Infrared Camera Technology[J]. Journal of Guangxi Normal University(Natural Science Edition), 2021, 39(1): 65 -70 .

Valuation on Compound Power Options under Double StochasticVolatility Jump Diffusion Model

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 7

Metrics

Comments

Recommended 10

[1]	WEN Yuzhuo, TANG Shengda, DENG Guohe. Analysis of the Ruin Time of Threshold Dividend Strategy Risk Model under Stochastic Environment [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 56-62.
[2]	WEN Yuzhuo, TANG Shengda, DENG Guohe. Asmussen’s Approach to Ruin Time of the Dependent Multi-typeRisk Processes in a Stochastic Environment [J]. Journal of Guangxi Normal University(Natural Science Edition), 2016, 34(3): 68-73.
[3]	WANG Jiaqin, DENG Guohe. Pricing of Interest Rate Derivatives Based on Affine Jump Diffusion Model [J]. Journal of Guangxi Normal University(Natural Science Edition), 2016, 34(3): 74-85.
[4]	XU Lei, DENG Guo-he. Valuation on European Lookback Option under Stochastic Volatility Model [J]. Journal of Guangxi Normal University(Natural Science Edition), 2015, 33(3): 79-90.
[5]	DENG Guo-he. Pricing European Chooser Options in Heston's Stochastic Volatility Model and Hedging Strategies [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(3): 36-43.
[6]	TANG Sheng-da, QIN Yong-song. Risk Process Driven by Markovian Environment Process [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(1): 35-39.
[7]	TANG Sheng-da, QIN Yong-song. Gerber-Shiu Function of MAP Risk Process Perturbedby Diffusion [J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(3): 23-27.