option pricing
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This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity, leptokurtic, and long memory, which indicate that the fractional calculus can describe the financial data well. Then, we investigate the option pricing under the assumption that the stock price is driven by the subordinated Brownian motion. The closed-form pricing formula for European options is derived. In the comparison with the classic Black–Sholes model, we find the option prices become higher, and the “volatility smiles” phenomenon happens in the proposed model. Finally, an empirical analysis is performed to show the validity of these results.

The reasonable pricing of options can effectively help investors avoid risks and obtain benefits, which plays a very important role in the stability of the financial market. The traditional single option pricing model often fails to meet the ideal expectations due to its limited conditions. Combining an economic model with a deep learning model to establish a hybrid model provides a new method to improve the prediction accuracy of the pricing model. This includes the usage of real historical data of about 10,000 sets of CSI 300 ETF options from January to December 2020 for experimental analysis. Aiming at the prediction problem of CSI 300ETF option pricing, based on the importance of random forest features, the Convolutional Neural Network and Long Short-Term Memory model (CNN-LSTM) in deep learning is combined with a typical stochastic volatility Heston model and stochastic interests CIR model in parameter models. The dual hybrid pricing model of the call option and the put option of CSI 300ETF is established. The dual-hybrid model and the reference model are integrated with ridge regression to further improve the forecasting effect. The results show that the dual-hybrid pricing model proposed in this paper has high accuracy, and the prediction accuracy is tens to hundreds of times higher than the reference model; moreover, MSE can be as low as 0.0003. The article provides an alternative method for the pricing of financial derivatives.

To estimate the parameters of the model of option pricing based on the model of rough fractional stochastic volatility (RFSV), we have carried out the empirical analysis during our study on the pricing of SSE 50ETF options in China. First, we have estimated the parameters of option pricing model by adopting the Monte Carlo simulation. Subsequently, we have empirically examined the pricing performance of the RFSV model by adopting the SSE 50ETF option price from January 2019 to December 2020. Our research findings indicate that by leveraging the RFSV model, we are able to attain a more accurate and stable level of option pricing than the conventional Black–Scholes (B-S) model on constant volatility. The errors of option pricing incurred by the B-S model proved to be larger and exhibited higher volatility, revealing the significant impact imposed by stochastic volatility on option pricing.