Variance Reduction Techniques Based on Binary Option Pricing
DOI:
https://doi.org/10.54097/hset.v49i.8532Keywords:
Control Variates; Antithetic Variates; Binary Option Pricing; Monte-Carlo Method.Abstract
Aiming at the binary option pricing model, control variates and antithetic variates methods are focused on comparing the reasons and influencing factors for the difference of variance reduction effect between them. By adjusting the independent variable of the control variates method and the range of binary options indication function, and by sensitivity analysis of four parameters of the pricing model, the study finds a way to improve the variance reduction ability. Through the detailed mathematical derivation of the antithetic variates method to confirm the law of the 4 parameters in the Black-Scholes model and the binary option price found by the former. And construct more accurate theoretical values to provide better direction for setting options prices in the real world.
Downloads
References
BlackF, ScholesM. The pricing of options and corporate liabilities [J]. Journal of Political Economy, 1973, 81(3): 637-654
CoxJ C, RossS A, Option pricing based on Alternative stochastic processes, Journal of Financial Economics,1976
CoxJ C, RossS A, RubinsteinM. Option pricing: a simplified approach [J]. Journal of Financial Economics, 1979, 9(7): 229-263
John C. Hull. Options, futures, and other derivatives [M]. A Simon & Schuster Company, 1997.416—417.
Thavaneswaran, A., Appadoo, S. S., & Frank, J. (2013). Binary option pricing using fuzzy numbers. Applied Mathematics Letters, 26(1), 65-72.
Gao, M. (2019) The British Binary Option. Journal of Mathematical Finance, 9, 747-762. doi: 10.4236/ jmf.2019.94038.
Mou G N. (2010). A comparative study on the application of Monte-Carlo method and quasi-Monte Carlo method in option pricing. Science Technology and Engineering (08),1925-1928+1933.
Liu G, Gu G D. (2014). American Option pricing based on Monte Carlo significance sampling method. Statistics and decision (09), 162-164. The doi: 10.13546 / j.carol carroll nki tjyjc. 2014.09.040.
Reuven Y. Rubinstein, Ruth Marcus, (1985) Efficiency of Multivariate Control Variates in Monte Carlo Simulation. Operations Research 33(3):661-677. http://dx.doi.org/10.1287/opre.33.3.661
Cao X L. (2015). The option pricing model and its variance reduction technique research (a master's degree thesis, Beijing university of chemical industry). https://kns.cnki.net/KCMS/detail/detail.aspx?dbname=CMFD201601&filename=1 015726296.nh
Boyle, P. P. (1977). Options: A monte carlo approach. Journal of financial economics, 4(3), 323-338.
Podlozhnyuk, V., & Harris, M. (2008). Monte carlo option pricing. CUDA SDK.
Ma Junhai, Zhang Wei, Liu Fengqin. Monte Carlo simulation comprehensive variance reduction technique for option pricing [J]. Journal of Management Science, 2005,8 (4): 68-73
Broadie M Detemple• Recent advances in numerical methods for pricing derivative secuities [A] · Numerical Methods in Finance [M] · Cambridge: Cambridge University Press, 1997. 170—229.
Bratley, P., Fox, B. L., & Schrage, L. E. (2011). A guide to simulation. Springer Science & Business Media.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
