Non-Gaussian VARMA model with stochastic volatility and applications in stock market bubbles

2019 ◽  
Vol 121 ◽  
pp. 129-136 ◽  
Author(s):  
Xiao-Li Gong ◽  
Xi-Hua Liu ◽  
Xiong Xiong ◽  
Xin-Tian Zhuang
Keyword(s):  
Stock Market ◽  
Stochastic Volatility ◽  
Stock Market Bubbles ◽  
Non Gaussian

A non-Gaussian stochastic volatility model

1998 ◽  
Vol 2 (2) ◽  
pp. 33-47 ◽  
Author(s):  
Yuichi Nagahara ◽  
Genshiro Kitagawa
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Non Gaussian

scholarly journals PRICING AND HEDGING OF VIX OPTIONS FOR BARNDORFF-NIELSEN AND SHEPHARD MODELS

2019 ◽  
Vol 22 (08) ◽  
pp. 1950043 ◽  
Author(s):  
TAKUJI ARAI
Keyword(s):  
Fourier Transform ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Option Price ◽  
Call Option ◽  
Stochastic Volatility Models ◽  
Risky Assets ◽  
Volatility Models ◽  
Vix Options ◽  
Non Gaussian

The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: non-Gaussian Ornstein–Uhlenbeck type stochastic volatility models. Moreover, we provide representations of the locally risk-minimizing strategy constructed by a combination of the underlying riskless and risky assets. Remark that the representations obtained in this paper are efficient to develop a numerical method using the fast Fourier transform. Thus, numerical experiments will be implemented in the last section of this paper.

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