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Reconstructing the Local Volatility Surface from Market Option Pricesopen access

Authors
Kwak, SoobinHwang, YoungjinChoi, YonghoWang, JianKim, SangkwonKim, Junseok
Issue Date
7월-2022
Publisher
MDPI
Keywords
Black-Scholes equations; finite difference method; local volatility function; option pricing
Citation
MATHEMATICS, v.10, no.14
Indexed
SCIE
SCOPUS
Journal Title
MATHEMATICS
Volume
10
Number
14
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/143394
DOI
10.3390/math10142537
ISSN
2227-7390
Abstract
We present an efficient and accurate computational algorithm for reconstructing a local volatility surface from given market option prices. The local volatility surface is dependent on the values of both the time and underlying asset. We use the generalized Black-Scholes (BS) equation and finite difference method (FDM) to numerically solve the generalized BS equation. We reconstruct the local volatility function, which provides the best fit between the theoretical and market option prices by minimizing a cost function that is a quadratic representation of the difference between the two option prices. This is an inverse problem in which we want to calculate a local volatility function consistent with the observed market prices. To achieve robust computation, we place the sample points of the unknown volatility function in the middle of the expiration dates. We perform various numerical experiments to confirm the simplicity, robustness, and accuracy of the proposed method in reconstructing the local volatility function.
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