Domain of influence of Local Volatility Function on the Solutions of the General Black-Scholes Equation

한국수학교육학회지시리즈B:순수및응용수학 / 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 (Department of Mathematics, Korea University)
Kim, Sangkwon (Department of Mathematics, Korea University)
Han, Hyunsoo (Department of Financial Engineering, Korea University)
Jang, Hanbyeol (Department of Financial Engineering, Korea University)
Lee, Chaeyoung (Department of Mathematics, Korea University)
Kim, Junseok (Department of Mathematics, Korea University)

Kim, Hyundong, Kim, Sangkwon, Han, Hyunsoo, Jang, Hanbyeol, Lee, Chaeyoung, & Kim, Junseok. (2020). DOMAIN OF INFLUENCE OF LOCAL VOLATILITY FUNCTION ON THE SOLUTIONS OF THE GENERAL BLACK-SCHOLES EQUATION. 한국수학교육학회지시리즈B:순수및응용수학, 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

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논문 상세

Vol.27 No.1

DOMAIN OF INFLUENCE OF LOCAL VOLATILITY FUNCTION ON THE SOLUTIONS OF THE GENERAL BLACK-SCHOLES EQUATION

Domain of influence of Local Volatility Function on the Solutions of the General Black-Scholes Equation

Abstract

한국수학교육학회지시리즈B:순수및응용수학