Technical gazette, Vol. 29 No. 4, 2022.
Original scientific paper
https://doi.org/10.17559/TV-20220406014211
A Lévy Option Pricing model of FFT-Based High-order Multinomial Tree
Wang Weiwei
orcid.org/0000-0001-6254-0692
; College of Economics and Management, Nanjing university of aeronautics and astronautics, Nanjing 211106, China; School of Applied Technology, Nanjing University of Information Science and Technology, Nanjing 210044, PR China
Li Bang Yi
; College of Economics and Management, Nanjing university of aeronautics and astronautics, Nanjing 211106, China
Hu Xiao Ping
orcid.org/0000-0002-0876-1037
; School of Economics and Management, Southeast University, Nanjing 210096 PR China
Abstract
This paper studies the method of constructing high order recombined multinomial tree based on fast Fourier transform (FFT), and applies multinomial tree option pricing under the Lévy process. First, the Lévy option pricing model and Fourier transform are introduced. Then, the network model based on FFT (Markov chain) is presented. After that, a method of constructing a recombined multinomial tree based on FFT is given. It is proved that the discrete random variables corresponding to the multinomial tree converge to the Lévy distributed continuous random variable. Next, we obtain the European option pricing formula of FFT multinomial tree pricing, and apply the reverse iteration method to the American option pricing. Finally, under the Jump-diffuse process, the difference between the computational accuracy and computational efficiency of the Semi-analytical solution of European Option and Merton European Call Option which are priced under FFT is compared. 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 derivative products.
Keywords
FFT; Lévy process; multinomial tree; option pricing
Hrčak ID:
279438
URI
Publication date:
17.6.2022.
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