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《Journal of Shantou University(Natural Science Edition)》 2019-01
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Pricing Binary Option Based on Fractional Brownian Motion and Stochastic Interest Rate Model

DENG Tingting;WEI Caimin;Department of Mathematics, Shantou University;  
The problem of pricing of underlying asset obeying fractional Brownian motion when the interest rate is assumed to obey Vasicek stochastic interest rate is studied. Firstly, the price of zero coupon bond is set. The partial differential equation satisfied by zero coupon bond is obtained, and the solution of affine structure that satisfies this partial differential equation is obtained. Then, using the hedging principle of the portfolio to construct the riskless asset, the partial differential equation satisfied by binary option in the fractional Vasicek stochastic interest rate model is obtained. Finally, appropriate combination of variables is introduced.Through many times in yuan handling, binary option of partial differential equation and its boundary condition are transformed into heat conduction equation to solve binary option formula.
【Fund】: 广东省自然科学基金项目(2017A030313005)
【CateGory Index】: O211.6;F830.9
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【Citations】
Chinese Journal Full-text Database 2 Hits
1 SUN Tian-yu,LIU Xin-ping(College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,Shaanxi,China);Binary option pricing model with transaction costs and the payment of dividend[J];陕西师范大学学报(自然科学版);2008-06
2 Zhang Juan Jin Zhiming(Department of system Engineering and Mathematics,National University of Defense Thechnology,Changsha,Hunan,410073);OPTION PRICING WITH STOCHASTIC INTEREST RATES[J];经济数学;2006-03
【Co-citations】
Chinese Journal Full-text Database 4 Hits
1 YU Xing,SUN Hong-guo(Hunan Institute of Humanities,Science and Technology,Loudi 417000);Fuzzy Pricing on AONC Option[J];长江大学学报(自然科学版);2011-07
2 ZHOU Hai-lin~1,WU Xin-yu~2,GAO Ling-yun~3,LU Feng-bin~4 (1.School of Finance,Anhui University of Finance and Economics,Bengbu 233030,China; 2.College of Business Administration,Hunan University,Changsha 410082,China; 3.Institute of World Economics and Politics,Chinese Academy of Social Science,Beijing 100732,China; 4.Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China);Pricing European options under stochastic interest rate[J];系统工程理论与实践;2011-04
3 SUN Li-juan(College of Science,Harbin Engineering University,Harbin,Heilongjiang,150001,China);European Option Pricing Based on Ornstein-Uhlenback Process under Stochastic Interest Rate[J];荆楚理工学院学报;2011-02
4 ZHANG Yun-liang1,MIAO Fang2,LIU Xin-ping2*(1 Department of Mathematics,Xi′an University of Art and Science,Xi′an 710065,Shaanxi,China;2 College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,Shaanxi,China);The foreign exchange option pricing of diffusion process with jumps[J];陕西师范大学学报(自然科学版);2009-06
【Secondary Citations】
Chinese Journal Full-text Database 5 Hits
1 ZHANG Li-na,LIU Xin-ping,NING Li-juan(College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,Shaanxi,China);Pricing of Bi-direction European options on stocks driven by Poisson jump diffusion process[J];陕西师范大学学报(自然科学版);2007-03
2 YANG Yun-feng, LIU Xin-ping(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China);Option pricing model about stock pricing jump process with compound Poisson process[J];陕西师范大学学报(自然科学版);2005-03
3 WANG Yang, XIAO Wen-ning, ZHANG Ji-zhou (Mathematics and Sciences College, Shanghai Normal University, Shanghai 200234, China);Pricing formulae for European options with transaction costs[J];上海师范大学学报(自然科学版);2005-01
4 LIU Qian, LIU Xin-ping (College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China);Option pricing about underlying asset pricing process by mixed process with transaction costs[J];陕西师范大学学报(自然科学版);2004-03
5 NING Lijuan, LIU Xinping(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China);Option pricing model when stock pricing process is a jimp-diffusion process[J];陕西师范大学学报(自然科学版);2003-04
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