A modification term for Black-Scholes model based on discrepancy calibrated with real market data

Xiaozheng Lin; Meiqing Wang; Choi-Hong Lai; Xiaozheng Lin; Meiqing Wang; Choi-Hong Lai

doi:10.3934/DSFE.2021017

Data Science in Finance and Economics

2021, Volume 1, Issue 4: 313-326. doi: 10.3934/DSFE.2021017

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Research article

A modification term for Black-Scholes model based on discrepancy calibrated with real market data

1.
School of Mathematics and Statistics, Fuzhou University, No.2. Wulongjiang North Avenue, Fuzhou, China
2.
School of Computing and Mathematical Sciences, University of Greenwich, SE10 9LS, London, UK

Received: 10 November 2021 Accepted: 16 December 2021 Published: 23 December 2021
JEL Codes: C63, C02

The Black-Scholes option pricing model (B-S model) generally requires the assumption that the volatility of the underlying asset be a piecewise constant. However, empirical analysis shows that there are discrepancies between the option prices obtained from the B-S model and the market prices. Most current modifications to the B-S model rely on modelling the implied volatility or interest rate. In contrast to the existing modifications to the Black-Scholes model, this paper proposes the concept of including a modification term to the B-S model itself. Using the actual discrepancies of the results of the Black-Scholes model and the market prices, the modification term related to the implied volatility is derived. Experimental results show that the modified model produces a better option pricing results when compare to market data.
- option pricing,
- black-scholes model,
- modification term,
- disturbance term,
- higher-order algorithm,
- second-order derivatives
Citation: Xiaozheng Lin, Meiqing Wang, Choi-Hong Lai. A modification term for Black-Scholes model based on discrepancy calibrated with real market data[J]. Data Science in Finance and Economics, 2021, 1(4): 313-326. doi: 10.3934/DSFE.2021017

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Abstract

The Black-Scholes option pricing model (B-S model) generally requires the assumption that the volatility of the underlying asset be a piecewise constant. However, empirical analysis shows that there are discrepancies between the option prices obtained from the B-S model and the market prices. Most current modifications to the B-S model rely on modelling the implied volatility or interest rate. In contrast to the existing modifications to the Black-Scholes model, this paper proposes the concept of including a modification term to the B-S model itself. Using the actual discrepancies of the results of the Black-Scholes model and the market prices, the modification term related to the implied volatility is derived. Experimental results show that the modified model produces a better option pricing results when compare to market data.

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