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Fuzzy LevyGJRGARCH American Option Pricing Model Based on an Infinite Pure Jump Process
Huiming ZHANG Junzo WATADA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E101D
No.7
pp.18431859 Publication Date: 2018/07/01 Publicized: 2018/04/16 Online ISSN: 17451361
DOI: 10.1587/transinf.2017EDP7236 Type of Manuscript: PAPER Category: Fundamentals of Information Systems Keyword: American option, fuzzy set theory, fuzzy simulation technology, Levy process, GJRGARCH model, least squares Monte Carlo approach, binomial tree method, quasirandom number, Brownian Bridge approach,
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Summary:
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 LevyGJRGARCH 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 shortterm options have higher precision than those of medium and longterm 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 quasirandom number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach.

