From (Martingale) Schrodinger Bridges to a New Class of Stochastic Volatility Model

2019 ◽  
Author(s):  
Pierre Henry-Labordere
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
New Class ◽  
Volatility Model

STOCHASTIC VOLATILITY MODEL WITH CORRELATED JUMP SIZES AND INDEPENDENT ARRIVALS

2020 ◽  
pp. 1-19
Author(s):  
Pengzhan Chen ◽  
Wuyi Ye
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Period Analysis ◽  
New Class ◽  
Volatility Models ◽  
Volatility Model ◽  
Article Study ◽  
Jump Sizes

In light of recent empirical research on jump activity, this article study the calibration of a new class of stochastic volatility models that include both jumps in return and volatility. Specifically, we consider correlated jump sizes and both contemporaneous and independent arrival of jumps in return and volatility. Based on the specifications of this model, we derive a closed-form relationship between the VIX index and latent volatility. Also, we propose a closed-form logarithmic likelihood formula by using the link to the VIX index. By estimating alternative models, we find that the general counting processes setting lead to better capturing of return jump behaviors. That is, the part where the return and volatility jump simultaneously and the part that jump independently can both be captured. In addition, the size of the jumps in volatility is, on average, positive for both contemporaneous and independent arrivals. However, contemporaneous jumps in the return are negative, but independent return jumps are positive. The sub-period analysis further supports above insight, and we find that the jumps in return and volatility increased significantly during the two recent economic crises.

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
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