Pricing Israeli Option with Time-changed Compensation by an FFT-Based High-order Multinomial Tree in Lévy Markets

The problem for pricing the Israel option with time-changed compensation was studied based on the high-order recombined multinomial tree by using a fast Fourier transform to approximate a Lévy process. First, the Lévy option pricing model and Fourier transform are introduced. Then, a network model based on FFT (Markov chain) is presented. After that, an FFT-based multinomial tree construction method is given to solve the problem of difficult parameter estimation when approximating the Lévy process with high-order multinomial trees. It is proved that the discrete random variables corresponding to the multinomial tree converge to the Lévy-distributed continuous random variable. Next, an algorithm based on a reverse recursion algorithm for pricing the Israel option with time-changed compensation was presented. Finally, an example was illustrated, and the relationship between the price of the Israel option and the time-changed compensation was discussed. The results show that the method of constructing a high-order recombined multinomial tree based on FFT has very high calculation precision and calculation speed, which can solve the problem of traditional risk-neutral multinomial tree construction, and it is a promising pricing method for pricing Israel options.