Factor Stochastic Volatility Model Research Articles

Pricing of defaultable options with multiscale generalized Heston’s stochastic volatility

The possibility of default risk of an option writer becomes a more important issue in over-the-counter option market when systemic risk increases. It is desirable for the option price to reflect the default risk. On the other hand, it is known that a single scale, single factor stochastic volatility model such as the well-known Heston model would not price correctly in- and out-of-the money options. So, this paper studies the pricing of defaultable options under a multiscale generalized Heston’s stochastic volatility model introduced by Fouque and Lorig (2011) to resolve these issues. We derive an explicit solution formula for the defaultable option price and investigate the characteristics of the resultant price in comparison to the price under the original Heston model.

Macroeconomic Uncertainty Through the Lens of Professional Forecasters

We analyze the evolution of macroeconomic uncertainty in the United States, based on the forecast errors of consensus survey forecasts of various economic indicators. Comprehensive information contained in the survey forecasts enables us to capture a real-time subjective measure of uncertainty in a simple framework. We jointly model and estimate macroeconomic (common) and indicator-specific uncertainties of four indicators, using a factor stochastic volatility model. Our macroeconomic uncertainty has three major spikes aligned with the 1973–75, 1980, and 2007–09 recessions, while other recessions were characterized by increases in indicator-specific uncertainties. We also show that the selection of data vintages affects the estimates and relative size of jumps in estimated uncertainty series. Finally, our macroeconomic uncertainty has a persistent negative impact on real economic activity, rather than producing “wait-and-see” dynamics.

Non-Stationary Stochastic Volatility Model for Dynamic Feedback and Skewness

In this paper I present a new single factor stochastic volatility model for asset return observed in discrete time and its latent volatility. This model unites the feedback effect and return skewness using a common factor for return and its volatility. Further, it generalizes the existing stochastic volatility framework with constant feedback to one with time varying feedback and as a consequence time varying skewness. However, presence of dynamic feedback effect violates the weak-stationarity assumption usually considered for the latent volatility process. The concept of bounded stationarity has been proposed in this paper to address the issue of non-stationarity. A characterization of the error distributions for returns and volatility is provided on the basis of existence of conditional moments. Finally, an application of the model has been explained using S&P100 daily returns under the assumption of Normal error and half Normal common factor distribution.

A common jump factor stochastic volatility model

We introduce a new multivariate stochastic volatility model, based on the presence of a latent common factor with random jumps. The common factor is parameterized as a permanent component using a compound binomial process. This model can capture common jumps in the latent volatilities between markets, with particular relevance in the presence of crises and contagion in emerging markets.

It's all about volatility of volatility: Evidence from a two-factor stochastic volatility model

The persistent nature of equity volatility is investigated by means of a multi-factor stochastic volatility model with time varying parameters. The parameters are estimated by means of a sequential matching procedure which adopts as an auxiliary model a time-varying generalization of the HAR model for the realized volatility series. It emerges that during the recent financial crisis the relative weight of the daily component dominates over the monthly term. The estimates of the two factor stochastic volatility model suggest that the change in the dynamic structure of the realized volatility during the financial crisis is due to the increase in the volatility of the persistent volatility term. A set of Monte Carlo simulations highlights the robustness of the methodology adopted in tracking the dynamics of the parameters. • We study the dynamics of the log-realized volatility with a time-varying HAR. • Parameters are estimated with an on-line method. • The parameters of a two-factor stochastic volatility model are recursively estimated. • The vol-of-vol parameter of the slow factor increases during the financial crisis. • The increase of vol-of-vol generates higher persistence and higher variability.

A Latent Factor Model of Multivariate Conditional Heteroscedasticity

This papers examines the joint dynamics of a system of asset returns. I describe and implement a multivariate factor stochastic volatility (MVFSV) model. I follow closely the work of Doz and Renault (2006), with two important changes. First, I design a sequential testing procedure to determine the dimensions of the appropriate factor structure needed to accommodate the conditional heteroscedasticity among a system of returns. Second, I employ a form of Tikhonov Regularization in order to overcome a near singularity among the moment conditions used for estimation. Simulation studies suggest that the MVFSV model is able to recover accurately the latent factors that drive the conditional volatility of returns. Moreover, the model estimates can be used to construct conditionally homoscedastic portfolios as linear combinations of the conditionally heteroscedastic assets. An empirical application to portfolios representing the twelve sectors of the U.S. economy

Factor stochastic volatility with time varying loadings and Markov switching regimes

We generalize the factor stochastic volatility (FSV) model of Pitt and Shephard [1999. Time varying covariances: a factor stochastic volatility approach (with discussion). In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statistics, vol. 6, Oxford University Press, London, pp. 547–570.] and Aguilar and West [2000. Bayesian dynamic factor models and variance matrix discounting for portfolio allocation. J. Business Econom. Statist. 18, 338–357.] in two important directions. First, we make the FSV model more flexible and able to capture more general time-varying variance–covariance structures by letting the matrix of factor loadings to be time dependent. Secondly, we entertain FSV models with jumps in the common factors volatilities through So, Lam and Li's [1998. A stochastic volatility model with Markov switching. J. Business Econom. Statist. 16, 244–253.] Markov switching stochastic volatility model. Novel Markov Chain Monte Carlo algorithms are derived for both classes of models. We apply our methodology to two illustrative situations: daily exchange rate returns [Aguilar, O., West, M., 2000. Bayesian dynamic factor models and variance matrix discounting for portfolio allocation. J. Business Econom. Statist. 18, 338–357.] and Latin American stock returns [Lopes, H.F., Migon, H.S., 2002. Comovements and contagion in emergent markets: stock indexes volatilities. In: Gatsonis, C., Kass, R.E., Carriquiry, A.L., Gelman, A., Verdinelli, I. Pauler, D., Higdon, D. (Eds.), Case Studies in Bayesian Statistics, vol. 6, pp. 287–302].

The Asymptotic Expansion Formula of Implied Volatility for Dynamic SABR Model and FX Hybrid Model

The author considers SABR model which is a two factor stochastic volatility model and gives an asymptotic expansion formula of implied volatilities for this model. His approach is based on infinite dimensional analysis on the Malliavin calculus and large deviation. Furthermore, he applies the approach to a foreign exchange model where interest rates and the FX volatilities are stochastic and gives an asymptotic expansion formula of implied volatilities of foreign exchange options.

Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model

We investigate the implications of time-varying expected return and volatility on asset allocation in a high dimensional setting. We propose a dynamic factor multivariate stochastic volatility (DFMSV) model that allows the first two moments of returns to vary over time for a large number of assets. We then evaluate the economic significance of the DFMSV model by examining the performance of various dynamic portfolio strategies chosen by mean-variance investors in a universe of 36 stocks. We find that the DFMSV dynamic strategies significantly outperform various benchmark strategies out of sample. This outperformance is robust to different performance measures, investor’s objective functions, time periods, and assets.

Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model

We investigate the implications of time-varying expected return and volatility on asset allocation in a high-dimensional setting. We propose a DFMSV model that allows the first two moments of returns to vary over time for a large number of assets. We then evaluate the economic significance of the DFMSV model by examining the performance of various dynamic portfolio strategies chosen by mean-variance investors in a universe of 36 stocks. We find that the DFMSV dynamic strategies significantly outperform various benchmark strategies out of sample. This outperformance is robust to different performance measures, investor's objective functions, time periods, and assets.

Spectral GMM estimation of continuous-time processes

Abstract This paper derives a methodology for the estimation of continuous-time stochastic models based on the characteristic function. The estimation method does not require discretization of the stochastic process, and it is simple to apply in practice. The method is essentially generalized method of moments on the complex plane. Hence it shares the efficiency and distribution properties of GMM estimators. We illustrate the method with some applications to relevant estimation problems in continuous-time Finance. We estimate a model of stochastic volatility, a jump–diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump–diffusion model. We find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution, while stochastic volatility is important to capture the overall level of this kurtosis. Positive jumps are not statistically significant once we allow for stochastic volatility in the model. We also estimate a non-affine model of stochastic volatility, and find that the power of the diffusion coefficient appears to be between one and two, rather than the value of one-half that leads to the standard affine stochastic volatility model. However, we find that including jumps into this non-affine, stochastic volatility model reduces the power of the diffusion coefficient to one-half. Finally, we offer an explanation for the observation that the estimate of persistence in stochastic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model.

Spectral GMM Estimation of Continuous-Time Processes

This paper derives a methodology for the exact estimation of continuous-time stochastic models based on the characteristic function. The estimation method does not require discretization of the process, and it is easy to apply. The method is essentially generalized method of moments on the complex plane. Hence it shares the optimality and distribution properties of GMM estimators. Moreover, we show that there are instruments that make the estimator asymptotically efficient. We illustrate the method with some applications to relevant estimation problems in continuous-time finance. We estimate a model of stochastic volatility, a jump-diffusion model with constant volatility and a model that nests both the stochastic volatility model and the jump-diffusion model. We find that negative jumps are important to explain skewness and asymmetry in excess kurtosis of the stock return distribution, while stochastic volatility is important to capture the overall level of this kurtosis. Positive jumps are not statistically significant once we allow for stochastic volatility in the model. We also estimate a non-affine model of stochastic volatility and we find that the power of the diffusion coefficient appears to be between one and two, rather than the value of one-half that leads to the standard affine stochatic volatility model. Finally, we offer an explanation for the observation that the estimate of persistence in stochatic volatility increases dramatically as the frequency of the observed data falls based on a multiple factor stochastic volatility model.

A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation

The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and log-normal jumps or constant jump intensity combined with a one factor stochastic volatility model. We introduce several generalizations which can better accommodate several empirical features of returns data. In their most general form we introduce a class of processes which nests jump-diffusions previously considered in empirical work and includes the affine class of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998) but also allows for non-affine random intensity jump components. We attain the generality of our specification through a generic Levy process characterization of the jump component. The processes we introduce share the desirable feature with the affine class that they yield analytically tractable and explicit option pricing formula. The non-affine class of processes we study include specifications where the random intensity jump component depends on the size of the previous jump which represent an alternative to affine random intensity jump processes which feature correlation between the stochastic volatility and jump component. We also allow for and experiment with different empirical specifications of the jump size distributions. We use two types of data sets. One involves the S&P500 and the other comprises of 100 years of daily Dow Jones index. The former is a return series often used in the literature and allows us to compare our results with previous studies. The latter has the advantage to provide a long time series and enhances the possibility of estimating the jump component more precisely. The non-affine random intensity jump processes are more parsimonious than the affine class and appear to fit the data much better.