Option pricing of geometric Asian options in a subdiffusive Brownian motion regime

Zhidong Guo; Xianhong Wang; Yunliang Zhang; Zhidong Guo; Xianhong Wang; Yunliang Zhang

doi:10.3934/math.2020342

AIMS Mathematics

2020, Volume 5, Issue 5: 5332-5343. doi: 10.3934/math.2020342

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Research article

Option pricing of geometric Asian options in a subdiffusive Brownian motion regime

1.
School of Mathematics and Physics, Anqing Normal University, Anqing, 246133, P. R. China
2.
School of Science, East China University of Technology, Nanchang, 330000, P. R. China

Received: 22 March 2020 Accepted: 17 June 2020 Published: 22 June 2020
MSC : 91B26, 60H10, 58J35

In this paper, pricing problem of the geometric Asian option in a subdiffusive Brownian motion regime is discussed. The subdiffusive property is manifested by the random periods of time, during which the asset price does not change. Subdiffusive partial differential equations for geometric Asian option are derived by using delta-hedging strategy. Explicit formula for geometric Asian option is obtained by using partial differential equation method. Furthermore, numerical studies are performed to illustrate the performance of our proposed pricing model.
- hedging,
- option pricing,
- subdiffusive process,
- asian option
Citation: Zhidong Guo, Xianhong Wang, Yunliang Zhang. Option pricing of geometric Asian options in a subdiffusive Brownian motion regime[J]. AIMS Mathematics, 2020, 5(5): 5332-5343. doi: 10.3934/math.2020342

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Abstract

In this paper, pricing problem of the geometric Asian option in a subdiffusive Brownian motion regime is discussed. The subdiffusive property is manifested by the random periods of time, during which the asset price does not change. Subdiffusive partial differential equations for geometric Asian option are derived by using delta-hedging strategy. Explicit formula for geometric Asian option is obtained by using partial differential equation method. Furthermore, numerical studies are performed to illustrate the performance of our proposed pricing model.

References

[1]	F. Black, M. Scholes, The pricing of options and corporate liabilities, J. Polit. Econ., 81 (1973), 637-654. doi: 10.1086/260062
[2]	I. Elizar, J. Klafler, Spatial gliding, temporal trapping and anomalous transport, Physica D, 187 (2004), 30-50. doi: 10.1016/j.physd.2003.09.023
[3]	M. Magdziarz, Black-Scholes formula in subdiffusive regime, J. Stat. Phys., 136 (2009), 553-564. doi: 10.1007/s10955-009-9791-4
[4]	J. R. Liang, J. Wang, L. J. Lv, et al. Fractional Fokker-Planck Equation and Black-Scholes Formula in Composite-Diffusive Regime, J. Stat. Phys., 146 (2012), 205-216. doi: 10.1007/s10955-011-0396-3
[5]	J. Wang, J. R. Liang, L. J. Lv, et al. Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime, Physica A, 391 (2012), 750-759. doi: 10.1016/j.physa.2011.09.008
[6]	M. Magdziarz, Option pricing in subdiffusive Bachelier model, J. Stat. Phys., 145 (2011), 187-203. doi: 10.1007/s10955-011-0310-z
[7]	Z. D. Guo, H. J. Yuan, Pricing European option under the time-changed mixed Brownian-fractional Brownian model, Physica A, 406 (2014), 73-79. doi: 10.1016/j.physa.2014.03.032
[8]	Z. D. Guo, Option pricing under the Merton model of short rate in subdiffusive Brownian motion regime, J. Stat. Comput. Sim., 87 (2017), 519-529. doi: 10.1080/00949655.2016.1218880
[9]	S. Orzeł, A. Wyłomańska, Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times, J. Stat. Phys., 143 (2011), 447-454. doi: 10.1007/s10955-011-0191-1
[10]	B. L. S. P. Rao, Pricing geometric Asian power options under mixed fractional Brownian motion enviroment, Physica A, 446 (2016), 92-99. doi: 10.1016/j.physa.2015.11.013
[11]	Z. J. Mao, Z. A. Liang, Evaluation of geometric Asian options under fractional Brownian motion, J. Math. Finac., 4 (2014), 1-9. doi: 10.4236/jmf.2014.41001
[12]	W. G. Zhang, Z. Li, Y. J. Liu, Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion, Physica A, 490 (2018), 402-418. doi: 10.1016/j.physa.2017.08.070
[13]	L. Xu, Ergodicity of the stochastic real Ginzburg-Landau equation driven by α-stable noises, Stoch. Proc. Appl., 123 (2013), 3710-3736. doi: 10.1016/j.spa.2013.05.002
[14]	X. Zhang, Derivative formulas and gradient estimates for SDEs driven by α-stable process, Stoch. Proc. Appl., 123 (2013), 1213-1228. doi: 10.1016/j.spa.2012.11.012
[15]	M. Magdziarz, Stochastic representation of subdiffusion processes with time-dependent drift, Stoch. Proc. Appl., 119 (2009), 3238-3252. doi: 10.1016/j.spa.2009.05.006
[16]	M. Magdziarz, Path properties of subdiffusion-a martingale approach, Stoch. Models, 26 (2010), 256-271. doi: 10.1080/15326341003756379

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