Research article

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

  • 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.

    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

    Related Papers:

  • 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.


    加载中


    [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
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3023) PDF downloads(259) Cited by(1)

Article outline

Figures and Tables

Figures(3)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog