A mixed PDE/Monte-Carlo method for stochastic volatility models

2009 ◽  
Vol 347 (9-10) ◽  
pp. 559-563 ◽  
Author(s):  
Grégoire Loeper ◽  
Olivier Pironneau
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stochastic Volatility ◽  
Stochastic Volatility Models ◽  
Volatility Models

scholarly journals Lattice Methods for Pricing American Strangles with Two-Dimensional Stochastic Volatility Models

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xuemei Gao ◽  
Dongya Deng ◽  
Yue Shan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stochastic Volatility ◽  
Least Square ◽  
Two Dimensional ◽  
Stochastic Volatility Models ◽  
Lattice Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Volatility Models

The aim of this paper is to extend the lattice method proposed by Ritchken and Trevor (1999) for pricing American options with one-dimensional stochastic volatility models to the two-dimensional cases with strangle payoff. This proposed method is compared with the least square Monte-Carlo method via numerical examples.

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 Hybrid Data Cloning Maximum Likelihood Estimator for Stochastic Volatility Models

2013 ◽  
Vol 5 (2) ◽  
pp. 193-229 ◽  
Author(s):  
Márcio Poletti Laurini
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Stochastic Volatility ◽  
Great Accuracy ◽  
Stochastic Volatility Models ◽  
Likelihood Estimator ◽  
Simulated Maximum Likelihood ◽  
Volatility Models ◽  
Data Cloning

Abstract: In this article, we analyze a maximum likelihood estimator using Data Cloning for Stochastic Volatility models. This estimator is constructed using a hybrid methodology based on Integrated Nested Laplace Approximations to calculate analytically the auxiliary Bayesian estimators with great accuracy and computational efficiency, without requiring the use of simulation methods such as Markov Chain Monte Carlo. We analyze the performance of this estimator compared to methods based on Monte Carlo simulations (Simulated Maximum Likelihood, MCMC Maximum Likelihood) and approximate maximum likelihood estimators using Laplace Approximations. The results indicate that this data cloning methodology achieves superior results over methods based on MCMC, comparable to results obtained by the Simulated Maximum Likelihood estimator. The methodology is extended to models with leverage effects, continuous time formulations, multifactor and multivariate stochastic volatility.

scholarly journals Estimating Stochastic Volatility under the Assumption of Stochastic Volatility of Volatility

Risks ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 35
Author(s):  
Moawia Alghalith ◽  
Christos Floros ◽  
Konstantinos Gkillas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Discrete Time ◽  
Simulation Analysis ◽  
Stochastic Volatility Models ◽  
Nonparametric Estimators ◽  
Volatility Models ◽  
Equity Index ◽  
Over Time

We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary over time. Our methods are exceedingly simple and far simpler than the existing ones. Using intraday prices for the Standard & Poor’s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of volatility are stochastic. We also proceeded in a Monte Carlo simulation analysis and found that the estimates were reasonably accurate. Such evidence implies that the stochastic volatility models proposed in the literature with constant volatility of volatility may fail to approximate the discrete-time short rate dynamics.

Sign in / Sign up

Export Citation Format

Share Document