European vulnerable options pricing under sub-mixed fractional jump-diffusion model with stochastic interest rate

With the development of financial markets, the trading of financial derivatives has become more flexible. To meet the demands of investors, over-the-counter (OTC) trading of options has also become increasingly frequent, raising concerns about accurately pricing vulnerable options. This study investigates the pricing problem of European vulnerable options under the sub-mixed fractional jump-diffusion (SMFJ) model. Firstly, the underlying asset price model and the counterparty company value model are established under the SMFJ model with a sub-mixed fractional Vasicek stochastic interest rate. Then, analytical solutions for the European vulnerable options are obtained using the quasi-martingale measure transformation and the risk-neutral pricing method. Additionally, the accuracy of the pricing formula is verified through the Monte Carlo simulation method. Finally, the rationality and validity of the established model are confirmed by numerical simulations, and the influence of key parameters on the pricing models is analyzed.