Abstract: Since the hypotheses of the classical Black-Scholes option pricing model ignore the impact of sudden change on asset prices and the "volatility smile" on the option value, particularly, it deviates from the actual situations. Many improvements of the Black-Scholes model are based on two directions: one is the option pricing model with jump-diffusion, and the other is the option pricing model with stochastic volatility. But very few researches combine these two factors into a model. In this paper, based on the previous work of the option pricing model with jumps or stochastic volatility, an improved option pricing model is firstly constructed by taking into account jump diffusion and stochastic volatility at the same time. The corresponding partial differential equation of the asset pricing, stochastic volatility and option pricing is derived by Ito lemma. Then, the stochastic distribution of asset price is obtained by the characteristic function method and Fourier transform approach. The numerical solution of the American option with jump diffusion and stochastic volatility is obtained by employing the Markov Chain approach. Finally, by the empirical research, the real option price of the patent of the project investment in a high-tech company is evaluated by using our developed model, and the effects of value changes of jump diffusion strength parameters and stochastic volatility parameters on the value of the patent option price are reported. It is concluded that the overvaluation of the patent option price, due to the ignorance of the uncertainty of the financial market, can be avoided effectively by introducing the jump-diffusion process of project profit and the stochastic volatility of market environment into the patent real option pricing model.

Key words: patent value, real option, jump-diffusion process, stochastic volatility, American option