Fuzzy Levy-GJR-GARCH American option pricing model based on an infinite pure jump process

Zhang, H. and Watada, J. (2018) Fuzzy Levy-GJR-GARCH American option pricing model based on an infinite pure jump process. IEICE Transactions on Information and Systems, E101D (7). pp. 1843-1859.

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Abstract

This paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium- and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach. © Copyright 2018 The Institute of Electronics Information and Communication Engineers.

Item Type: Article
Impact Factor: cited By 0
Uncontrolled Keywords: Bridge approaches; Costs; Curve fitting; Economics; Electronic trading; Financial markets; Fuzzy set theory; Fuzzy sets; Least squares approximations; Markov processes; Membership functions; Numerical methods; Stochastic models; Stochastic systems, American options; Binomial tree method; Brownian bridge; Fuzzy simulation; GJR-GARCH models; Least squares monte carlo; Levy process; Quasi-random numbers, Monte Carlo methods
Depositing User: Mr Ahmad Suhairi Mohamed Lazim
Date Deposited: 26 Feb 2019 02:26
Last Modified: 26 Feb 2019 02:26
URI: http://scholars.utp.edu.my/id/eprint/20817

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