The Improvement of Implied Volatility of Black-Scholes Model: A Review

DOI

10.2991/aebmr.k.220405.102How to use a DOI?

Keywords

Black-Scholes Model; Implied Volatility; BS model

Abstract

The Black-Scholes model used in the financial industry can predict the price of the option and thus construct the hedging portfolio to avoid the risk. However, the model assumes the implied volatility to be constant, which cannot fit the curve of real market volatility, which causes inaccuracy in prediction and causes loss for practitioners. To solve the problem, mathematicians and economists add randomness to parameters of the volatility in the BS model. However, each model has its limitation. In this paper, we reviewed relative research of BS model, and two possible improvements of BS model, the local volatility function model and stochastic model, to fit the implied volatility to the real volatility surface, the volatility smile. In addition to that, we discuss the limitations of both models, where the stochastic model can predict forward volatility when the options have long maturities while behaving poorly at predicting short-term volatility. The local volatility function model has similar but opposite limitations. It can only precisely predict the short-term volatility, while the long maturity volatility surface shows flatten with a little variant. Thus, we introduce a possible improvement to consist of the strength of both the Local volatility function model and the stochastic volatility model, though it has its own limitation on the processing speed and strict requirement of the parameters.

Copyright

© 2022 The Authors. Published by Atlantis Press International B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license.

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TY  - CONF
AU  - Fanghao Ye
PY  - 2022
DA  - 2022/04/29
TI  - The Improvement of Implied Volatility of Black-Scholes Model: A Review
BT  - Proceedings of the 2022 7th International Conference on Social Sciences and Economic Development (ICSSED 2022)
PB  - Atlantis Press
SP  - 619
EP  - 623
SN  - 2352-5428
UR  - https://doi.org/10.2991/aebmr.k.220405.102
DO  - 10.2991/aebmr.k.220405.102
ID  - Ye2022
ER  -