Pricing Variance and Volatility Swaps in a Stochastic Volatility Model with Regime Switching: Discrete Observations Case

2012 ◽  
Author(s):  
Guang-Hua Lian ◽  
Robert J. R. Elliott
Keyword(s):  
Stochastic Volatility ◽  
Regime Switching ◽  
Stochastic Volatility Model ◽  
Discrete Observations ◽  
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 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.

scholarly journals Option pricing in a regime switching stochastic volatility model

2018 ◽  
Vol 138 ◽  
pp. 116-126 ◽  
Author(s):  
Arunangshu Biswas ◽  
Anindya Goswami ◽  
Ludger Overbeck
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Regime Switching ◽  
Stochastic Volatility Model ◽  
Volatility Model

scholarly journals Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Xuerong Mao ◽  
Aubrey Truman ◽  
Chenggui Yuan
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Stochastic Volatility ◽  
Regime Switching ◽  
Stochastic Systems ◽  
Stochastic Volatility Model ◽  
Explicit Solutions ◽  
New Techniques ◽  
Volatility Model ◽  
Mathematical Difficulties

Stochastic differential equations (SDEs) under regime-switching have recently been developed to model various financial quantities. In general, SDEs under regime-switching have no explicit solutions, so numerical methods for approximations have become one of the powerful techniques in the valuation of financial quantities. In this paper, we will concentrate on the Euler-Maruyama (EM) scheme for the typical hybrid mean-reverting θ-process. To overcome the mathematical difficulties arising from the regime-switching as well as the non-Lipschitz coefficients, several new techniques have been developed in this paper which should prove to be very useful in the numerical analysis of stochastic systems.

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