Stochastic volatility model with regime-switching skewness in heavy-tailed errors for exchange rate returns

2013 ◽  
Vol 17 (5) ◽  
Author(s):  
Jouchi Nakajima
Keyword(s):  
Exchange Rate ◽  
Stochastic Volatility ◽  
Regime Switching ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Heavy Tailed

scholarly journals VARIANCE AND VOLATILITY SWAPS UNDER A TWO-FACTOR STOCHASTIC VOLATILITY MODEL WITH REGIME SWITCHING

2019 ◽  
Vol 22 (04) ◽  
pp. 1950009
Author(s):  
XIN-JIANG HE ◽  
SONG-PING ZHU
Keyword(s):  
Markov Chain ◽  
Characteristic Function ◽  
Stochastic Volatility ◽  
Regime Switching ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Significant Difference ◽  
Cir Process

In this paper, the pricing problem of variance and volatility swaps is discussed under a two-factor stochastic volatility model. This model can be treated as a two-factor Heston model with one factor following the CIR process and another characterized by a Markov chain, with the motivation originating from the popularity of the Heston model and the strong evidence of the existence of regime switching in real markets. Based on the derived forward characteristic function of the underlying price, analytical pricing formulae for variance and volatility swaps are presented, and numerical experiments are also conducted to compare swap prices calculated through our formulae and those obtained under the Heston model to show whether the introduction of the regime switching factor would lead to any significant difference.

scholarly journals A Locally Both Leptokurtic and Fat-Tailed Distribution with Application in a Bayesian Stochastic Volatility Model

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 689
Author(s):  
Łukasz Lenart ◽  
Anna Pajor ◽  
Łukasz Kwiatkowski
Keyword(s):  
Stochastic Volatility ◽  
Latent Variables ◽  
Financial Time Series ◽  
Stochastic Volatility Model ◽  
Mcmc Methods ◽  
Statistical Framework ◽  
Typical Data ◽  
Volatility Model ◽  
Density Forecasting ◽  
Heavy Tailed

In the paper, we begin with introducing a novel scale mixture of normal distribution such that its leptokurticity and fat-tailedness are only local, with this “locality” being separately controlled by two censoring parameters. This new, locally leptokurtic and fat-tailed (LLFT) distribution makes a viable alternative for other, globally leptokurtic, fat-tailed and symmetric distributions, typically entertained in financial volatility modelling. Then, we incorporate the LLFT distribution into a basic stochastic volatility (SV) model to yield a flexible alternative for common heavy-tailed SV models. For the resulting LLFT-SV model, we develop a Bayesian statistical framework and effective MCMC methods to enable posterior sampling of the parameters and latent variables. Empirical results indicate the validity of the LLFT-SV specification for modelling both “non-standard” financial time series with repeating zero returns, as well as more “typical” data on the S&P 500 and DAX indices. For the former, the LLFT-SV model is also shown to markedly outperform a common, globally heavy-tailed, t-SV alternative in terms of density forecasting. Applications of the proposed distribution in more advanced SV models seem to be easily attainable.

scholarly journals Modeling Precious Metal Returns through Fractional Jump-Diffusion Processes Combined with Markov Regime-Switching Stochastic Volatility

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 407
Author(s):  
Martha Carpinteyro ◽  
Francisco Venegas-Martínez ◽  
Alí Aali-Bujari
Keyword(s):  
Decision Making ◽  
Stochastic Volatility ◽  
Regime Switching ◽  
Precious Metal ◽  
Precious Metals ◽  
Stochastic Volatility Model ◽  
Decision Making Process ◽  
Markov Regime Switching ◽  
Volatility Model ◽  
Gold Silver

This paper is aimed at developing a stochastic volatility model that is useful to explain the dynamics of the returns of gold, silver, and platinum during the period 1994–2019. To this end, it is assumed that the precious metal returns are driven by fractional Brownian motions, combined with Poisson processes and modulated by continuous-time homogeneous Markov chains. The calibration is carried out by estimating the Jump Generalized Autoregressive Conditional Heteroscedasticity (Jump-GARCH) and Markov regime-switching models of each precious metal, as well as computing their Hurst exponents. The novelty in this research is the use of non-linear, non-normal, multi-factor, time-varying risk stochastic models, useful for an investors’ decision-making process when they intend to include precious metals in their portfolios as safe-haven assets. The main empirical results are as follows: (1) all metals stay in low volatility most of the time and have long memories, which means that past returns have an effect on current and future returns; (2) silver and platinum have the largest jump sizes; (3) silver’s negative jumps have the highest intensity; and (4) silver reacts more than gold and platinum, and it is also the most volatile, having the highest probability of intensive jumps. Gold is the least volatile, as its percentage of jumps is the lowest and the intensity of its jumps is lower than that of the other two metals. Finally, a set of recommendations is provided for the decision-making process of an average investor looking to buy and sell precious metals.

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