A triple-threshold leverage stochastic volatility model

2015 ◽  
Vol 19 (4) ◽  
Author(s):  
Xin-Yu Wu ◽  
Hai-Lin Zhou
Keyword(s):  
Monte Carlo ◽  
Stock Market ◽  
Stochastic Volatility ◽  
Value At Risk ◽  
Leverage Effect ◽  
Model Parameters ◽  
Finite Sample ◽  
Financial Return ◽  
Proposed Model ◽  
Volatility Model

AbstractIn this paper we introduce a triple-threshold leverage stochastic volatility (TTLSV) model for financial return time series. The main feature of the model is to allow asymmetries in the leverage effect as well as mean and volatility. In the model the asymmetric effect is modeled by a threshold nonlinear structure that the two regimes are determined by the sign of the past returns. The model parameters are estimated using maximum likelihood (ML) method based on the efficient importance sampling (EIS) technique. Monte Carlo simulations are presented to examine the accuracy and finite sample properties of the proposed methodology. The EIS-based ML (EIS-ML) method shows good performance according to the Monte Carlo results. The proposed model and methodology are applied to two stock market indices for China. Strong evidence of the mean and volatility asymmetries is detected in Chinese stock market. Moreover, asymmetries in the volatility persistence and leverage effect are also discovered. The log-likelihood and Akaike information criterion (AIC) suggest evidence in favor of the proposed model. In addition, model diagnostics suggest that the proposed model performs relatively well in capturing the key features of the data. Finally, we compare models in a Value at Risk (VaR) study. The results show that the proposed model can yield more accurate VaR estimates than the alternatives.

Estimation of SV Model with Leverage Effect Based on MCMC Technique

2014 ◽  
Vol 530-531 ◽  
pp. 605-608
Author(s):  
Xiao Cui Yin
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stock Index ◽  
Leverage Effect ◽  
Model Parameters ◽  
Convergence Diagnostics ◽  
Volatility Model ◽  
Mcmc Simulation ◽  
Series Convergence

This paper is to study the estimation of stochastic volatility model with leverage effect using Bayesian approach and Markov Chain Monte Carlo (MCMC) simulation technique. The data used is China's Shenzheng stock index. Estimations of model parameters are achieved by using MCMC technique in Openbugs Software, results show that there is leverage effect in Shenzheng stock series, convergence diagnostics suggest that parameters of the model are convergent.

scholarly journals Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Guohe Deng
Keyword(s):  
Stochastic Volatility ◽  
Diffusion Model ◽  
Implied Volatility ◽  
Empirical Work ◽  
Jump Diffusion ◽  
Model Parameters ◽  
Single Factor ◽  
Proposed Model ◽  
Volatility Model ◽  
Jump Diffusion Model

Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model in which two variance processes with jumps drive the underlying stock price and then considers the valuation on European style option. We derive a semianalytical formula for European vanilla option and develop a fast and accurate numerical algorithm for the computation of the option prices using the fast Fourier transform (FFT) technique. We compare the volatility smile and probability density of the proposed model with those of alternative models, including the normal jump diffusion model and single-factor stochastic volatility model with jumps, respectively. Finally, we provide some sensitivity analysis of the model parameters to the options and several calibration tests using option market data. Numerical examples show that the proposed model has more flexibility to capture the implied volatility term structure and is suitable for empirical work in practice.

scholarly journals A LOW-BIAS SIMULATION SCHEME FOR THE SABR STOCHASTIC VOLATILITY MODEL

2012 ◽  
Vol 15 (02) ◽  
pp. 1250016 ◽  
Author(s):  
BIN CHEN ◽  
CORNELIS W. OOSTERLEE ◽  
HANS VAN DER WEIDE
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Realistic Model ◽  
Stochastic Volatility Model ◽  
Model Parameters ◽  
Fixed Income ◽  
Financial Industry ◽  
Volatility Model ◽  
Discretization Schemes ◽  
Simulation Scheme

The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.

Bayesian Semi-Parametric Realized Conditional Autoregressive Expectile Models for Tail Risk Forecasting

2020 ◽  
Author(s):  
Richard Gerlach ◽  
Chao Wang
Keyword(s):  
Value At Risk ◽  
Model Parameters ◽  
Model Framework ◽  
Measurement Equation ◽  
Asset Return ◽  
Proposed Model ◽  
Asymmetric Least Squares ◽  
Least Squares Optimization ◽  
Conditional Autoregressive ◽  
Improved Accuracy

Abstract A new model framework called Realized Conditional Autoregressive Expectile is proposed, whereby a measurement equation is added to the conventional Conditional Autoregressive Expectile model. A realized measure acts as the dependent variable in the measurement equation, capturing the contemporaneous dependence between it and the latent conditional expectile; it also drives the expectile dynamics. The usual grid search and asymmetric least squares optimization, to estimate the expectile level and parameters, suffers from convergence issues leading to inefficient estimation. This article develops an alternative random walk Metropolis stochastic target search method, incorporating an adaptive Markov Chain Monte Carlo sampler, which leads to improved accuracy in estimation of the expectile level and model parameters. The sampling properties of this method are assessed via a simulation study. In a forecast study applied to several market indices and asset return series, one-day-ahead Value-at-Risk and Expected Shortfall forecasting results favor the proposed model class.

scholarly journals INTEGRAL REPRESENTATION OF PROBABILITY DENSITY OF STOCHASTIC VOLATILITY MODELS AND TIMER OPTIONS

2017 ◽  
Vol 20 (08) ◽  
pp. 1750055 ◽  
Author(s):  
ZHENYU CUI ◽  
J. LARS KIRKBY ◽  
GUANGHUA LIAN ◽  
DUY NGUYEN
Keyword(s):  
Stochastic Volatility ◽  
Probabilistic Method ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Model Parameters ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Probability Densities ◽  
Special Case

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767–785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, [Formula: see text], and a special case of the [Formula: see text]-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The [Formula: see text]-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472–1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the [Formula: see text] model and a special case of the [Formula: see text]-Hypergeometric model.

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