Correlated continuous time random walk and option pricing

In this paper, we study a correlated continuous time random walk (CCTRW) with averaged waiting time, whose probability density function (PDF) is proved to follow stretched Gaussian distribution. Then, we apply this process into option pricing problem. Supposing the price of the underlying is driven by this CCTRW, we find this model captures the subdiffusive characteristic of financial markets. By using the mean self-financing hedging strategy, we obtain the closed-form pricing formulas for a European option with and without transaction costs, respectively. At last, comparing the obtained model with the classical Black–Scholes model, we find the price obtained in this paper is higher than that obtained from the Black–Scholes model. A empirical analysis is also introduced to confirm the obtained results can fit the real data well.