TY - JOUR
T1 - Reconstruction of the local volatility function using the Black–Scholes model
AU - Kim, Sangkwon
AU - Han, Hyunsoo
AU - Jang, Hanbyeol
AU - Jeong, Darae
AU - Lee, Chaeyoung
AU - Lee, Wonjin
AU - Kim, Junseok
N1 - Funding Information:
The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have significantly improved the quality of this paper. The corresponding author (J.S. Kim) was supported by the National Research Foundation (NRF), Korea, under project BK21 FOUR.
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/4
Y1 - 2021/4
N2 - In this paper, we propose a robust and accurate numerical algorithm to reconstruct a local volatility function using the Black–Scholes (BS) partial differential equation (PDE). Using the BS PDE and given market data, option prices at strike prices and expiry times, a time-dependent local volatility function is computed. The proposed algorithm consists of the following steps: (1) The time-dependent volatility function is computed using a recently developed method; (2) A Monte Carlo simulation technique is used to find the effective region which has a strong influence on option prices; and we partition the effective domain into several sub-regions and define a local volatility function based on the time-dependent volatility function on the sub-regions; and (3) Finally, we calibrate the local volatility function using the fully implicit finite difference method and the conjugate gradient optimization algorithm. We demonstrate the robustness and accuracy of the proposed local volatility reconstruction algorithm using manufactured volatility surface and real market data.
AB - In this paper, we propose a robust and accurate numerical algorithm to reconstruct a local volatility function using the Black–Scholes (BS) partial differential equation (PDE). Using the BS PDE and given market data, option prices at strike prices and expiry times, a time-dependent local volatility function is computed. The proposed algorithm consists of the following steps: (1) The time-dependent volatility function is computed using a recently developed method; (2) A Monte Carlo simulation technique is used to find the effective region which has a strong influence on option prices; and we partition the effective domain into several sub-regions and define a local volatility function based on the time-dependent volatility function on the sub-regions; and (3) Finally, we calibrate the local volatility function using the fully implicit finite difference method and the conjugate gradient optimization algorithm. We demonstrate the robustness and accuracy of the proposed local volatility reconstruction algorithm using manufactured volatility surface and real market data.
KW - Black–Scholes equation
KW - Finite difference method
KW - Local volatility
KW - Monte Carlo simulation
UR - http://www.scopus.com/inward/record.url?scp=85102292911&partnerID=8YFLogxK
U2 - 10.1016/j.jocs.2021.101341
DO - 10.1016/j.jocs.2021.101341
M3 - Article
AN - SCOPUS:85102292911
SN - 1877-7503
VL - 51
JO - Journal of Computational Science
JF - Journal of Computational Science
M1 - 101341
ER -