scholarly journals Regime-switching stochastic volatility model: estimation and calibration to VIX options

2017 ◽  
Vol 24 (1) ◽  
pp. 38-75 ◽  
Author(s):  
Stéphane Goutte ◽  
Amine Ismail ◽  
Huyên Pham
Keyword(s):  
Stochastic Volatility ◽  
Regime Switching ◽  
Stochastic Volatility Model ◽  
Model Estimation ◽  
Vix Options ◽  
Volatility Model

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 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>

Pricing Bermudan Variance Swaptions Using Multinomial Trees

2019 ◽  
Keyword(s):  
Stochastic Volatility ◽  
Fair Value ◽  
Stochastic Volatility Model ◽  
Realized Variance ◽  
Variance Swaps ◽  
Early Exercise ◽  
Numerical Tests ◽  
Vix Options ◽  
Vix Futures ◽  
Volatility Model

In a recent study, Zhao et al. (2017) presented a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model; it provided an efficient way of calculating the fair value of the strike for variance swaps. In this article, the authors expand the methodology to price nonlinear derivatives written on realized variance. They introduce a new option contract, a Bermudan variance swaption, defined as an option on variance swap with early exercise dates. Within the same framework they also show how to value forward-start variance swaps, VIX futures, and VIX options. Numerical tests show that the methodology is efficient and accurate.

Joint pricing of VIX and SPX options with stochastic volatility and jump models

2015 ◽  
Vol 16 (1) ◽  
pp. 27-48 ◽  
Author(s):  
Thomas Kokholm ◽  
Martin Stisen
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Option Markets ◽  
Content Type ◽  
Volatility Index ◽  
Vix Options ◽  
Vix Futures ◽  
Volatility Model ◽  
Joint Pricing

Purpose – This paper studies the performance of commonly employed stochastic volatility and jump models in the consistent pricing of The CBOE Volatility Index (VIX) and The S&P 500 Index (SPX) options. With the existence of active markets for volatility derivatives and options on the underlying instrument, the need for models that are able to price these markets consistently has increased. Although pricing formulas for VIX and vanilla options are now available for commonly used models exhibiting stochastic volatility and/or jumps, it remains to be shown whether these are able to price both markets consistently. This paper fills this vacuum. Design/methodology/approach – In particular, the Heston model, the Heston model with jumps in returns and the Heston model with simultaneous jumps in returns and variance (SVJJ) are jointly calibrated to market quotes on SPX and VIX options together with VIX futures. Findings – The full flexibility of having jumps in both returns and volatility added to a stochastic volatility model is essential. Moreover, we find that the SVJJ model with the Feller condition imposed and calibrated jointly to SPX and VIX options fits both markets poorly. Relaxing the Feller condition in the calibration improves the performance considerably. Still, the fit is not satisfactory, and we conclude that one needs more flexibility in the model to jointly fit both option markets. Originality/value – Compared to existing literature, we derive numerically simpler VIX option and futures pricing formulas in the case of the SVJ model. Moreover, the paper is the first to study the pricing performance of three widely used models to SPX options and VIX derivatives.

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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