The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Cet article se concentre principalement sur les questions liées à la tarification des options américaines dans un environnement flou en prenant en compte le regroupement de la volatilité des prix des actifs sous-jacents, de l'effet de levier et des sauts stochastiques. En traitant la volatilité comme un nombre flou parabolique, nous avons construit un modèle de Levy-GJR-GARCH basé sur un processus de saut pur infini et avons combiné le modèle avec une technologie de simulation floue pour effectuer des simulations numériques basées sur l'approche des moindres carrés de Monte Carlo et le binôme flou. méthode arborescente. Une étude empirique a été réalisée à partir des données américaines sur les options de vente de l'indice Standard & Poor's 100. Les résultats sont les suivants : dans un environnement flou, le résultat de la valorisation des options est plus précis que celui dans un environnement clair, les simulations de prix des options à court terme ont une plus grande précision que celles des options à moyen et long terme, L'approche des moindres carrés de Monte Carlo donne une évaluation plus précise que la méthode de l'arbre binomial flou, et les effets de simulation des différents processus de Levy indiquent que les modèles NIG et CGMY sont supérieurs au modèle VG. De plus, le prix des options augmente à mesure que le délai d'expiration des options s'allonge et que le prix d'exercice augmente, la courbe de la fonction d'adhésion est asymétrique avec une tendance inclinée à gauche et l'intervalle flou se rétrécit à mesure que le niveau fixé α et l'exposant de la fonction d'adhésion n augmenter. De plus, les résultats démontrent que les approches des nombres quasi-aléatoires et du pont brownien peuvent améliorer la vitesse de convergence de l'approche des moindres carrés de Monte Carlo.
Huiming ZHANG
Waseda University
Junzo WATADA
PETRONAS University of Technology
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Huiming ZHANG, Junzo WATADA, "Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process" in IEICE TRANSACTIONS on Information,
vol. E101-D, no. 7, pp. 1843-1859, July 2018, doi: 10.1587/transinf.2017EDP7236.
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.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2017EDP7236/_p
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@ARTICLE{e101-d_7_1843,
author={Huiming ZHANG, Junzo WATADA, },
journal={IEICE TRANSACTIONS on Information},
title={Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process},
year={2018},
volume={E101-D},
number={7},
pages={1843-1859},
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.},
keywords={},
doi={10.1587/transinf.2017EDP7236},
ISSN={1745-1361},
month={July},}
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TY - JOUR
TI - Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process
T2 - IEICE TRANSACTIONS on Information
SP - 1843
EP - 1859
AU - Huiming ZHANG
AU - Junzo WATADA
PY - 2018
DO - 10.1587/transinf.2017EDP7236
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E101-D
IS - 7
JA - IEICE TRANSACTIONS on Information
Y1 - July 2018
AB - 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.
ER -