Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method

2016 ◽  
Vol 03 (04) ◽  
pp. 1650030
Author(s):  
Mengzhe Zhang ◽  
Leunglung Chan
Keyword(s):  
Stochastic Volatility ◽  
Approximation Method ◽  
Regime Switching ◽  
Saddlepoint Approximation ◽  
Stochastic Volatility Model ◽  
Approximation Formula ◽  
Chain Process ◽  
Volatility Model ◽  
Highly Nonlinear ◽  
The Given

Pricing a volatility swap is a highly nonlinear problem. Explicit solutions of the prices of volatility swaps are notoriously difficult to find. In this paper, we consider a saddlepoint approximation method for the valuation of a volatility swap under the Heston’s stochastic volatility model with regime switching. All the values of key parameters in our model are supposed to depend on the states of a continuous time observable Markov chain process. We present a closed-form exact cumulant generating functions (CGFs) of the continuous realized variance. Additionally, an approximated CGF is given. Then we approximate the volatility swaps by the saddlepoint approximation formula which derived from the Fourier inversion representation. The numerical results suggest that the alternative saddlepoint approximation method (ASAP) and the approximated ASAP method could both produce fairly accurate results for the given range of maturities.

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.

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