Stochastic volatility and the mean reverting process

2002 ◽  
Vol 23 (1) ◽  
pp. 33-47 ◽  
Author(s):  
Sotirios Sabanis
Keyword(s):  
Stochastic Volatility ◽  
The Mean ◽  
Mean Reverting Process

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 Volatility in International Stock Markets: An Empirical Study during COVID-19

2020 ◽  
Vol 13 (9) ◽  
pp. 208
Author(s):  
Rashmi Chaudhary ◽  
Priti Bakhshi ◽  
Hemendra Gupta
Keyword(s):  
Econometric Model ◽  
Central Tendency ◽  
International Stock Markets ◽  
Efficient Portfolios ◽  
The Mean ◽  
Garch Modeling ◽  
Autoregressive Conditional Heteroscedasticity ◽  
Bounce Back ◽  
Daily Returns ◽  
Mean Reverting Process

Predicting volatility is a must in the finance domain. Estimations of volatility, along with the central tendency, permit us to evaluate the chances of getting a particular result. Financial analysts are frequently challenged with the assignment of diversifying assets in order to form efficient portfolios with a higher risk to reward ratio. The objective of this research is to analyze the influence of COVID-19 on the return and volatility of the stock market indices of the top 10 countries based on GDP using a widely applied econometric model—generalized autoregressive conditional heteroscedasticity (GARCH). For this purpose, the daily returns of market indices from January 2019 to June 2020 were taken into consideration. The results reveal daily negative mean returns for all market indices during the COVID period (January 2020 to June 2020). Though the second quarter of the COVID period reflects a bounce back for all market indices with altered strengths, the volatility remains higher than in normal periods, signaling a bearish tendency in the market. The COVID variable, as an exogenous variance regressor in GARCH modeling, is found to be positive and significant for all market indices. Furthermore, the results confirmed the mean-reverting process for all market indices.

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.

scholarly journals Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Chaoqun Ma ◽  
Shengjie Yue ◽  
Yishuai Ren
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Option Price ◽  
Closed Form Solution ◽  
European Option ◽  
Short Term ◽  
Underlying Asset ◽  
Asset Value ◽  
Mean Reverting Process

This paper considers the pricing issue of vulnerable European option when the dynamics of the underlying asset value and counterparty’s asset value follow two correlated exponential Lévy processes with stochastic volatility, and the stochastic volatility is divided into the long-term and short-term volatility. A mean-reverting process is introduced to describe the common long-term volatility risk in underlying asset price and counterparty’s asset value. The short-term fluctuation of stochastic volatility is governed by a mean-reverting process. Based on the proposed model, the joint moment generating function of underlying log-asset price and counterparty’s log-asset value is explicitly derived. We derive a closed-form solution for the vulnerable European option price by using the Fourier inversion formula for distribution functions. Finally, numerical simulations are provided to illustrate the effects of stochastic volatility, jump risk, and counterparty credit risk on the vulnerable option price.

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