scholarly journals An application of the hybrid Monte Carlo algorithm for realized stochastic volatility model

2016 ◽  
Author(s):  
Tetsuya Takaishi ◽  
Yu-Bin Liu ◽  
Ting Ting Chen
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Monte Carlo Algorithm ◽  
Hybrid Monte Carlo ◽  
Volatility Model

scholarly journals BAYESIAN INFERENCE OF STOCHASTIC VOLATILITY MODEL BY HYBRID MONTE CARLO

2009 ◽  
Vol 18 (08) ◽  
pp. 1381-1396 ◽  
Author(s):  
TETSUYA TAKAISHI
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Bayesian Inference ◽  
Stochastic Volatility ◽  
Metropolis Algorithm ◽  
Stochastic Volatility Model ◽  
Financial Data ◽  
Stock Index ◽  
Hybrid Monte Carlo ◽  
Volatility Model

The hybrid Monte Carlo (HMC) algorithm is applied for the Bayesian inference of the stochastic volatility (SV) model. We use the HMC algorithm for the Markov chain Monte Carlo updates of volatility variables of the SV model. First we compute parameters of the SV model by using the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC algorithm decorrelates the volatility variables faster than the Metropolis algorithm. Second we make an empirical study for the time series of the Nikkei 225 stock index by the HMC algorithm. We find the similar correlation behavior for the sampled data to the results from the artificial financial data and obtain a ϕ value close to one (ϕ ≈ 0.977), which means that the time series has the strong persistency of the volatility shock.

scholarly journals A note on stochastic volatility model estimation

2019 ◽  
Vol 17 (4) ◽  
pp. 22
Author(s):  
Omar Abbara ◽  
Mauricio Zevallos
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Parameter Estimates ◽  
Model Estimation ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Monte Carlo Evaluation

<p>The paper assesses the method proposed by Shumway and Stoffer (2006, Chapter 6, Section 10) to estimate the parameters and volatility of stochastic volatility models. First, the paper presents a Monte Carlo evaluation of the parameter estimates considering several distributions for the perturbations in the observation equation. Second, the method is assessed empirically, through backtesting evaluation of VaR forecasts of the S&amp;P 500 time series returns. In both analyses, the paper also evaluates the convenience of using the Fuller transformation.</p>

A control variate method for weak approximation of SDEs via discretization of numerical error of asymptotic expansion

2019 ◽  
Vol 25 (3) ◽  
pp. 239-252
Author(s):  
Yusuke Okano ◽  
Toshihiro Yamada
Keyword(s):  
Monte Carlo ◽  
Asymptotic Expansion ◽  
Stochastic Volatility ◽  
Diffusion Processes ◽  
Stochastic Volatility Model ◽  
Weak Approximation ◽  
Numerical Examples ◽  
Control Variate ◽  
Volatility Model ◽  
Multidimensional Diffusion

Abstract The paper shows a new weak approximation method for stochastic differential equations as a generalization and an extension of Heath–Platen’s scheme for multidimensional diffusion processes. We reformulate the Heath–Platen estimator from the viewpoint of asymptotic expansion. The proposed scheme is implemented by a Monte Carlo method and its variance is much reduced by the asymptotic expansion which works as a kind of control variate. Numerical examples for the local stochastic volatility model are shown to confirm the efficiency of the method.

scholarly journals CAM Stochastic Volatility Model for Option Pricing

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Wanwan Huang ◽  
Brian Ewald ◽  
Giray Ökten
Keyword(s):  
Monte Carlo ◽  
Characteristic Function ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
The Other ◽  
Stochastic Volatility Models ◽  
Control Variate ◽  
Volatility Models ◽  
Volatility Model ◽  
Cam Model

The coupled additive and multiplicative (CAM) noises model is a stochastic volatility model for derivative pricing. Unlike the other stochastic volatility models in the literature, the CAM model uses two Brownian motions, one multiplicative and one additive, to model the volatility process. We provide empirical evidence that suggests a nontrivial relationship between the kurtosis and skewness of asset prices and that the CAM model is able to capture this relationship, whereas the traditional stochastic volatility models cannot. We introduce a control variate method and Monte Carlo estimators for some of the sensitivities (Greeks) of the model. We also derive an approximation for the characteristic function of the model.

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