关键词: 4/2-CIR随机混合模型, 期权定价, 快速傅里叶变换, 敏感性分析

Abstract: With the increasing number of endogenous and exogenous shocks, the financial market has entered an unprecedented period of instability, which increases the financial market risk. As an important financial derivative product, option can effectively hedge the market risk, and the key to using option to hedge the market risk is to price it reasonably. The core of the research on option pricing is to construct a model that fits in with the dynamic change characteristics of the underlying asset. The uncertainty of the future of the financial market keeps the price of financial assets appreciated or depreciated, that is, the volatility of the underlying asset price of the option is not a definite constant but has a certain degree of volatility. Therefore, in order to ensure the reliability of the option pricing results, in the process of constructing the pricing model we must take into account the stochastic volatility characteristics of the underlying asset price. In addition, with the continuous change in national economic policies and financial market conditions, the market interest rate is no longer a constant. An accurate description of the stochastic characteristics of market interest rates is conducive to improving the pricing accuracy of financial derivatives. Therefore, how to accurately describe the dynamic process of financial asset prices and the stochastic fluctuation characteristics of interest rates is an urgent problem to be solved.
   In this paper, we fully consider the dynamic change characteristics of financial asset prices and the impact of interest rate stochasticity on the pricing results of the option pricing model, and explore the option pricing problem under the 4/2 stochastic volatility model with stochastic interest rate under the assumption that the volatility obeys the mean-reverting process. Firstly, based on the dynamic characteristics of financial asset prices and the randomness of interest rates, the 4/2-CIR stochastic hybrid model is constructed, and the characteristic function of the underlying log asset price and the European option pricing formula based on the 4/2-CIR model are obtained using It’s formula and fast Fourier transform methods. Secondly, a numerical analysis is conducted based on the 4/2-CIR stochastic hybrid model to explore the impact of interest rate stochasticity on the model pricing results, and a sensitivity analysis is conducted on the main parameters in the 4/2-CIR stochastic hybrid model to study the impact of model parameters on the option pricing results. Finally, based on the SSE 50 ETF options market data, the particle swarm optimization algorithm is used to estimate the unknown parameters in the model, and the pricing accuracy and error of the model are analyzed based on the model parameter estimation.
   The results show that: the larger the maturity period, the more obvious the impact of interest rate stochastic characteristics on the pricing results of the model, that is, under the stochastic volatility model, to consider the impact of the interest rate factor on the pricing of options is of great practical significance. The speed of mean reversion in volatility and interest rates, as well as changes in the level of mean reversion, moves in the opposite direction of option price movements. The volatility of volatility has a positive effect on option prices. The volatility of interest rates has a non-significant effect on option prices. In conclusion, the stochastic interest rate has a significant effect on the model pricing results. The option price is insensitive to the volatility parameter of interest rate, while it is more sensitive to all other parameters. In addition, the 4/2-CIR stochastic hybrid model has smaller absolute error, mean square error and average absolute percentage error and more accurate pricing results than the classical B-S model and the 4/2 stochastic volatility model.

Key words: 4/2-CIR stochastic hybrid model, option pricing, fast Fourier transform, sensitivity analysis