### Data Science in Finance and Economics

2021, Issue 4: 313-326. doi: 10.3934/DSFE.2021017
Research article

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

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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