Fractional integrated GARCH diffusion limit models

In this paper, we introduce an approximate approach to the fractional integrated GARCH(1,1) model of continuous time perturbed by fractional noise. Based on the $L^2$-approximation of this noise by semimartingales, we proved a convergence theorem concerning an approximate solution. A simulation example shows a significant reduction of error in a fractional stock price model as compared to the classical stock price model.     

GARCH-type forecasting models for volatility of stock market and MCS test

The prediction of time-changing volatility is an important task in the modeling of financial data. In the paper, a comprehensive analysis of the mean return and conditional variance of SSE380 index is performed to use GARCH, EGARCH and TGARCH models with Normal innovation and Student's t innovation. Conducting a bootstrap simulation study which shows the Model Confidence Set (MCS) captures the superior models across a range of significance levels. The experimental results show that, under various loss functions, the GARCH using Student's t innovation model is the best model for volatility predictions of SSE380 among the six models.     

Option pricing for a stochastic volatility Lévy model with stochastic interest rates

An alternative option pricing model under a forward measure is proposed, in which asset prices follow a stochastic volatility Lévy model with stochastic interest rate. The stochastic interest rate is driven by the Hull–White process. By using an approximate method, we find a formulation for the European option in term of the characteristic function of the tail probabilities.     

Value at risk estimation under stochastic volatility models using adaptive PMCMC methods

In this paper, we propose a value-at-risk (VaR) estimation technique based on a new stochastic volatility model with leverage effect, nonconstant conditional mean and jump. In order to estimate the model parameters and latent state variables, we integrate the particle filter and adaptive Markov Chain Monte Carlo (MCMC) algorithms to develop a novel adaptive particle MCMC (A-PMCMC) algorithm. Comprehensive simulation experiments based on three stock indices and two foreign exchange time series show effectiveness of the proposed A-PMCMC algorithm and the VaR estimation technique.