scholarly journals The mean‐reverting 4/2 stochastic volatility model: Properties and financial applications

2020 ◽  
Vol 36 (5) ◽  
pp. 836-856
Author(s):  
Marcos Escobar‐Anel ◽  
Zhenxian Gong
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Financial Applications ◽  
Volatility Model ◽  
The Mean

scholarly journals Approximating Explicitly the Mean-Reverting CEV Process

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
N. Halidias ◽  
I. S. Stamatiou
Keyword(s):  
Stochastic Volatility ◽  
Diffusion Coefficients ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Financial Mathematics ◽  
Two Dimensional ◽  
Nonnegative Solutions ◽  
Volatility Model ◽  
Cev Process ◽  
The Mean

We are interested in the numerical solution of mean-reverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form(xt)q,where1/2<q<1. Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameterq. Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the two-dimensional stochastic volatility model with instantaneous variance process given by the above mean-reverting CEV process.

scholarly journals PERHITUNGAN VALUE AT RISK DENGAN PENDUGA VOLATILITAS STOKASTIK HESTON

2018 ◽  
Vol 7 (4) ◽  
pp. 317
Author(s):  
DESAK PUTU DEVI DAMIYANTI ◽  
KOMANG DHARMAWAN ◽  
LUH PUTU IDA HARINI
Keyword(s):  
At Risk ◽  
Stochastic Process ◽  
Stochastic Volatility ◽  
Value At Risk ◽  
Financial Risk ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
The Mean ◽  
Simulation Results

Value at risk is a method that measures financial risk of an security or portfolio. The aims of the research is to find out the value at risk of an exchange rate using the Heston stochastic volatility model. Heston model is a strochastic volatility model that assumes that volatility of the security follow stochastic process and consider the mean reversion. Based on simulation results, the value of volatility using Heston volatility estimastor is 0.2887, and the value of Heston VaR with 95 percent confident level is 0.0297. Based on result of backtesting,  there are 48 violations obtained VaR using Heston model, while historical VaR there are 2 violations. Thus, VaR using Heston model is more strict in estimating risk.

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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