Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (6): 1514-1531.
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Received:
2018-04-02
Online:
2019-12-26
Published:
2019-12-28
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CLC Number:
Zhaoqiang Yang. Pricing European Lookback Option in a Special Kind of Mixed Jump-Diffusion Black-Scholes Model[J].Acta mathematica scientia,Series A, 2019, 39(6): 1514-1531.
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股价 | 精确值 | ||||||
10 | 71.419978523 | 73.636156468 | 76.519896751 | 81.145748979 | 84.912047501 | 88.658351421 | 87.5310 |
20 | 63.260586024 | 65.223576189 | 67.777862873 | 71.875233511 | 75.211250358 | 78.529556890 | 77.5310 |
30 | 55.101193512 | 56.810995913 | 59.035828989 | 62.604718032 | 65.510453213 | 68.400762361 | 67.5310 |
40 | 46.941801092 | 48.398415621 | 50.293795111 | 53.334202565 | 55.809656065 | 58.271967823 | 57.5310 |
50 | 38.782408511 | 39.985835343 | 41.551761231 | 44.063687088 | 46.108858922 | 48.143173289 | 47.5310 |
60 | 30.623016001 | 31.573255065 | 32.809727353 | 34.793171621 | 36.408061771 | 38.014378764 | 37.5310 |
70 | 22.464439443 | 23.161516031 | 24.068567676 | 25.523583232 | 26.708234734 | 27.886597117 | 27.5320 |
80 | 14.368445442 | 14.814301500 | 15.394459401 | 16.325099631 | 17.082812751 | 17.836503307 | 17.6097 |
90 | 7.057221764 | 7.276208938 | 7.561159943 | 8.018254242 | 8.390413468 | 8.760596967 | 8.6492 |
"
股价 | 精确值 | ||||||
10 | 67.386870055 | 71.018366151 | 76.238252122 | 83.309467972 | 86.150639011 | 89.728816161 | 87.5310 |
20 | 59.688240989 | 62.904855955 | 67.528394784 | 73.791757867 | 76.308338686 | 79.477726082 | 77.5310 |
30 | 51.989611921 | 54.791345753 | 58.818537464 | 64.274047874 | 66.466038363 | 69.226636056 | 67.5310 |
40 | 44.290982862 | 46.677835544 | 50.108680141 | 54.756337743 | 56.623738038 | 58.975546033 | 57.5310 |
50 | 36.592353837 | 38.564325343 | 41.398822822 | 45.238627682 | 46.781437737 | 48.724456004 | 47.5310 |
60 | 28.893724747 | 30.450815141 | 32.688965565 | 35.720917626 | 36.939137373 | 38.473365978 | 37.5310 |
70 | 21.195865544 | 22.338116291 | 23.979979171 | 26.204159333 | 27.097821272 | 28.223301060 | 27.5320 |
80 | 13.557054821 | 14.287648062 | 15.337797447 | 16.760401881 | 17.331995611 | 18.051862002 | 17.6097 |
90 | 6.658698249 | 7.017537244 | 7.533329792 | 8.232057784 | 8.512802401 | 8.866372785 | 8.6492 |
1 |
Elliott J , Hoek J . A general fractional white noise theory and applications to finance. Mathematical Finance, 2003, 13 (2): 301- 330
doi: 10.1111/1467-9965.00018 |
2 |
Hu Y Z , Øsendal B . Fractional White noise calculus and applications to finance, infinite dimensional analysis. Quantum Probability and Related Topics, 2003, 6 (1): 1- 32
doi: 10.1142/S0219025703001110 |
3 | Mishura Y . Stochastic Calculus Fractional Brownian Motions and Related Processes. Berlin: Springer, 2008 |
4 |
Tomas B , Henrik H . A note on Wick products and the fractional Black-Scholes model. Finance and Stochastics, 2005, 9 (2): 197- 209
doi: 10.1007/s00780-004-0144-5 |
5 |
Xiao W L , Zhang W G , Zhang X L , Zhang X . Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm. Physica A, 2012, 391 (24): 6418- 6431
doi: 10.1016/j.physa.2012.07.041 |
6 |
Sun L . Pricing currency options in the mixed fractional Brownian motion. Physica A, 2013, 392 (16): 3441- 3458
doi: 10.1016/j.physa.2013.03.055 |
7 | He X J , Chen W T . The pricing of credit default swaps under a generalized mixed fractional Brownian motion. Physica A, 2014, 404 (36): 26- 33 |
8 |
Cheridito P . Mixed fractional Brownian motion. Bernoulli, 2001, 7 (6): 913- 934
doi: 10.2307/3318626 |
9 | Zili M. On the mixed fractional Brownian motion. Journal of Applied Mathematics and Stochastic Analysis, 2006, 1-9: Art ID: 32435 |
10 |
Bender C , Sottinen T , Valkeila E . Pricing by hedging and no-arbitrage beyond semimartingales. Finance and Stochastics, 2008, 12 (4): 441- 468
doi: 10.1007/s00780-008-0074-8 |
11 | Foad S , Adem K . Pricing currency option in a mixed fractional Brownian motion with jumps environment. Mathematical Problems in Engineering, 2014, 1 (1): 1- 13 |
12 | Foad S , Adem K . Actuarial approach in a mixed fractional Brownian motion with jumps environment for pricing currency option. Advances in Difference Equations, 2015, 257 (1): 1- 8 |
13 |
Rao B L S P . Option pricing for processes driven by mixed fractional Brownian motion with superimposed jumps. Probability in the Engineering and Informational Sciences, 2015, 29 (4): 589- 596
doi: 10.1017/S0269964815000200 |
14 |
Miao J , Yang X . Pricing model for convertible bonds:A mixed fractional Brownian motion with jumps. East Asian Journal on Applied Mathematics, 2015, 5 (3): 222- 237
doi: 10.4208/eajam.221214.240415a |
15 | Yang Z Q . Optimal exercise boundary of American fractional lookback option in a mixed jump-diffusion fractional Brownian motion environment. Mathematical Problems in Engineering, 2017, 3 (1): 1- 17 |
16 | 张伟江. 奇异摄动导论. 北京: 科学出版社, 2014 |
Zhang W J . Introduction to Singular Perturbation. Beijing: Science Press, 2014 | |
17 |
Nesterov A V , Shuliko O V . Asymptotics of the solution to a singularly perturbed system of parabolic equations in the critical case. Computational Mathematics and Mathematical Physics, 2010, 50 (2): 256- 263
doi: 10.1134/S0965542510020077 |
18 |
Ma Y S , Li Y . A uniform asymptotic expansion for stochastic volatility model in pricing multi-asset European options. Applied Stochastic Models in Business and Industry, 2012, 28 (4): 324- 341
doi: 10.1002/asmb.880 |
19 | Butuzov V F , Bychkov A I . Asymptotics of the solution of an initial-boundary value problem for a singularly perturbed parabolic equation in the case of double root of the degenerate equation. Computational Mathematics and Mathematical Physics, 2013, 49 (10): 1261- 1273 |
20 |
Lai T L , Lim T W . Exercise regions and efficient valuation of American lookback options. Mathematical Finance, 2004, 14 (2): 249- 269
doi: 10.1111/j.0960-1627.2004.00191.x |
21 |
Eberlein E , Papapantoleon A . Equivalence of floating and fixed strike Asian and lookback options. Stochastic Processes and their Applications, 2005, 115 (1): 31- 40
doi: 10.1016/j.spa.2004.07.003 |
22 |
Leung K S . An analytic pricing formula for lookback options under stochastic volatility. Applied Mathematics Letters, 2013, 26 (1): 145- 149
doi: 10.1016/j.aml.2012.07.008 |
23 |
Park S H , Kim J H . An semi-analytic pricing formula for lookback options under a general stochastic volatility model. Statistics and Probability Letters, 2013, 83 (11): 2537- 2543
doi: 10.1016/j.spl.2013.08.002 |
24 |
Fuh C D , Luo S F , Yen J F . Pricing discrete path-dependent options under a double exponential jump-diffusion model. Journal of Banking and Finance, 2013, 37 (8): 2702- 2713
doi: 10.1016/j.jbankfin.2013.03.023 |
25 |
杨朝强. 一类特殊混合跳-扩散模型的欧式回望期权定价. 华东师范大学学报(自然科学版), 2017, 194 (4): 1- 17
doi: 10.3969/j.issn.1000-5641.2017.04.001 |
Yang Z Q . Pricing European lookback option by a special kind of mixed jump-diffusion model. Journal of East China Normal University (Natural Science), 2017, 194 (4): 1- 17
doi: 10.3969/j.issn.1000-5641.2017.04.001 |
|
26 |
杨朝强. 混合跳-扩散模型下一类基金公司的金融债券定价与违约概率研究. 系统工程, 2018, 36 (2): 16- 28
doi: 10.3969/j.issn.1001-2362.2018.02.007 |
Yang Z Q . Pricing of fund corporate bonds and default probability study under mixed jump-diffusion model. Systems Engineering, 2018, 36 (2): 16- 28
doi: 10.3969/j.issn.1001-2362.2018.02.007 |
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