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ISSN : 1226-0657

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Vol.27 No.1
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Domain of influence of Local Volatility Function on the Solutions of the General Black-Scholes Equation

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2020, v.27 no.1, pp.43-50
https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.1.43
Kim, Hyundong
Kim, Sangkwon
Han, Hyunsoo
Jang, Hanbyeol
Lee, Chaeyoung
Kim, Junseok
Kim,, H. , Kim,, S. , Han,, H. , Jang,, H. , Lee,, C. , & Kim,, J. (2020). Domain of influence of Local Volatility Function on the Solutions of the General Black-Scholes Equation. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 27(1), 43-50, https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.1.43
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Abstract

We investigate the domain of influence of the local volatility function on the solutions of the general Black-Scholes model. First, we generate the sample paths of underlying asset using the Monte Carlo simulation. Next, we define the inner and outer domains to find the effective volatility region. To confirm the effect of the inner domain, we use the root mean square error for the European call option prices, and then change the values of volatility in the proposed domain. The computational experiments confirm that there is an effective region which dominates the option pricing.

keywords
local volatility function, general Black-Scholes equation, finite difference method

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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