Regime-switching Stochastic Volatility Model Research Articles

A closed-form pricing formula for forward start options under a regime-switching stochastic volatility model

Abstract In this paper, we consider the pricing problem of forward start options in the presence of stochastic volatility and regime-switching. By making use of the measure transform technique, with the underlying price as a new numeraire, a closed-form pricing formula is derived in which the only unknown term is the so-called forward characteristic function of the underlying price. The analytical expression of the forward characteristic function under the new measure is subsequently obtained in two steps; the first step treats the regime-switching Heston model as a time-dependent Heston model with the information of the Markov chain beingassumed to be given in advance, while the second step takes the expectation with respect to the Markov chain. Finally, the influence of introducing regime-switching into the Heston model is investigated to show the difference in terms of forward start option pricing between the two models.

Does the Financial Leverage Effect Depend on Volatility Regimes?

This paper investigates how the financial leverage effect changes across different volatility regimes. To test for regime dependency in the leverage effect, we introduce a new regime switching stochastic volatility model and apply the model to daily Standard and Poor’s 500 and NASDAQ return data. Our empirical analysis that uses Bayesian inference reveals that the leverage effect is reinforced when financial markets enter into high or medium-high volatility regimes.

A high-order RBF-FD method for option pricing under regime-switching stochastic volatility models with jumps

In this paper, we develop a high-order radial basis function finite difference (RBF-FD) approximation on a five-point stencil for pricing options under the regime-switching stochastic volatility models with log-normal and contemporaneous jumps (SVCJ). We fully exploit the capabilities of the RBF-FD to perform the interpolation, differentiation and integration approximations tasks required in the numerical solution of the SVCJ pricing partial integro-differential equation (PIDE). The resulting systems of equations are sparse and our treatment of the non-local integro discretisation allows an efficient implementation based on the fast Fourier transform (FFT) algorithm. We show that a local mesh refinement strategy gives high-order convergent solutions for both the European and the path dependent barrier option prices.

Option pricing in a regime switching stochastic volatility model

We consider a regime switching stochastic volatility model where the stock volatility dynamics is a semi-Markov modulated square root mean reverting process. Under this model assumption, we find the locally risk minimizing price of European type vanilla options. The price function is shown to satisfy a non-local degenerate parabolic PDE which can be viewed as a generalization of the Heston PDE. The related Cauchy problem involving the PDE is shown to be equivalent to an integral equation (IE). The existence and uniqueness of solution to the PDE is carried out by studying the IE and using the semigroup theory.

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

ABSTRACTWe develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a Cox–Ingersoll–Ross process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum–Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices.

Pricing and Hedging in Stochastic Volatility Regime Switching Models

We consider general regime switching stochastic volatility models where both the asset and the volatility dynamics depend on the values of a Markov jump process. Due to the stochastic volatility and the Markov regime switching, this financial market is thus incomplete and perfect pricing and hedging of options are not possible. Thus, we are interested in finding formulae to solve the problem of pricing and hedging options in this framework. For this, we use the local risk minimization approach to obtain pricing and hedging formulae based on solving a system of partial differential equations. Then we get also formulae to price volatility and variance swap options on these general regime switching stochastic volatility models.

Particle Filters for Markov Switching Stochastic Volatility Models

This paper proposes an auxiliary particle filter algorithm for inference in regime switching stochastic volatility models in which the regime state is governed by a first-order Markov chain. We proposes an ongoing updated Dirichlet distribution to estimate the transition probabilities of the Markov chain in the auxiliary particle filter. A simulation-based algorithm is presented for the method which demonstrated that we are able to estimate a class of models in which the probability that the system state transits from one regime to a different regime is relatively high. The methodology is implemented to analyze a real time series: the foreign exchange rate of Australian dollars vs South Korean won.

Regime-switching stochastic volatility: Evidence from the crude oil market

This paper incorporates regime-switching into the stochastic volatility (SV) framework in an attempt to explain the behavior of crude oil prices in order to forecast their volatility. More specifically, it models the volatility of oil return as a stochastic volatility process whose mean is subject to shifts in regime. The shift is governed by a two-state first-order Markov process. The Bayesian Markov Chain Monte Carlo method is used to estimate the models. The main findings are: first, there is clear evidence of regime-switching in the oil market. Ignoring it will lead to a false impression that the volatility is highly persistent and therefore highly predictable. Second, incorporating regime-switching into the SV framework significantly enhances the forecasting power of the SV model. Third, the regime-switching stochastic volatility model does a good job in capturing major events affecting the oil market.

Regime shifts in interest rate volatility

Abstract I find evidence of regime shifts in interest rate volatility using short-rate data from the U.S., the U.K., Japan, and Canada. The regime shifts, if unaccounted for, could lead to spurious volatility persistence when the volatility processes are estimated with the stochastic volatility (SVOL) model. In contrast, the apparent persistence in volatility drops sharply in three out of the four countries when I estimate the volatility processes with the regime-switching stochastic volatility (RSSV) model. I also contribute to the literature by showing how to account for correlation in the regime-switching stochastic volatility model, which is important for modeling asymmetric volatility.

Modeling long memory in stock market volatility

Inspired by the idea that regime switching may give rise to persistence that is observationally equivalent to a unit root, we derive a regime switching process that exhibits long memory. The feature of the process that generates long memory is a heavy-tailed duration distribution. Using this process for volatility, we obtain a regime switching stochastic volatility (RSSV) model that we fit to daily S&P returns from 1928 through 1995 by means of the efficient method of moments estimation (EMM) method. Forecasts of RSSV volatility given past returns can be generated by reprojection, as we illustrate. The RSSV model is accepted according to the EMM chi-squared statistic. Using this statistic, we also evaluate several other models that have been proposed in the literature and some modifications to them. We find that models that exhibit long memory in volatility and heavy tails conditionally, as does the RSSV model, fit the data, whereas models without these characteristics do not. We also find weak evidence that suggests the presence of an additional short memory component of volatility over and above the long memory component.