Maximum likelihood estimation of non-affine volatility processes

In this paper we develop a new estimation method for extracting non-affine latent stochastic volatility and risk premia from measures of model-free realized and risk-neutral integrated volatility. We estimate non-affine models with nonlinear drift and constant elasticity of variance and we compare them to the popular square-root stochastic volatility model. Our empirical findings are: (1) the square-root model is misspecified; (2) the inclusion of constant elasticity of variance and nonlinear drift captures stylized facts of volatility dynamics and (3) the square-root stochastic volatility model is explosive under the risk-neutral probability measure.     

A statistical comparison of the short-term interest rate models for Japan,U.S., and Germany

We propose a simple and practical model selection method for continuous time models. We apply the method to several continuous time short-term interest rate models using discrete time series data of Japan, U.S. and Germany. All the models can be easily estimated from discrete observations, and their performances can be evaluated in a uniform statistical framework. The models that allow dependence of volatility on the level of interest rates tend to perform well empirically. The degree of volatility dependence on the interest rate levels seems to be different across the countries. For the German data, we observe that a model with nonlinear drift performs better than the best linear drift model.     

A maximum likelihood approach to volatility estimation for a Brownian motion using high,low and close price data

Abstract

Volatility plays an important role in derivatives pricing, asset allocation, and risk management, to name but a few areas. It is therefore crucial to make the utmost use of the scant information typically available in short time windows when estimating the volatility. We propose a volatility estimator using the high and the low information in addition to the close price, all of which are typically available to investors. The proposed estimator is based on a maximum likelihood approach. We present explicit formulae for the likelihood of the drift and volatility parameters when the underlying asset is assumed to follow a Brownian motion with constant drift and volatility. Our approach is to then maximize this likelihood to obtain the estimator of the volatility. While we present the method in the context of a Brownian motion, the general methodology is applicable whenever one can obtain the likelihood of the volatility parameter given the high, low and close information. We present simulations which indicate that our estimator achieves consistently better performance than existing estimators (that use the same information and assumptions) for simulated data. In addition, our simulations using real price data demonstrate that our method produces more stable estimates. We also consider the effects of quantized prices and discretized time.     

Modelling conditional heteroscedasticity and jumps in Australian short-term interest rates

The present paper explores a class of jump–diffusion models for the Australian short‐term interest rate. The proposed general model incorporates linear mean‐reverting drift, time‐varying volatility in the form of LEVELS (sensitivity of the volatility to the levels of the short‐rates) and generalized autoregressive conditional heteroscedasticity (GARCH), as well as jumps, to match the salient features of the short‐rate dynamics. Maximum likelihood estimation reveals that pure diffusion models that ignore the jump factor are mis‐specified in the sense that they imply a spuriously high speed of mean‐reversion in the level of short‐rate changes as well as a spuriously high degree of persistence in volatility. Once the jump factor is incorporated, the jump models that can also capture the GARCH‐induced volatility produce reasonable estimates of the speed of mean reversion. The introduction of the jump factor also yields reasonable estimates of the GARCH parameters. Overall, the LEVELS–GARCH–JUMP model fits the data best.     

Nonlinear Drift And Stochastic Volatility: An Empirical Investigation Of Short-Term Interest Rate Models

In this article I provide new evidence on the role of nonlinear drift and stochastic volatility in interest rate modeling. I compare various model specifications for the short‐term interest rate using the data from five countries. I find that modeling the stochastic volatility in the short rate is far more important than specifying the shape of the drift function. The empirical support for nonlinear drift is weak with or without the stochastic volatility factor. Although a linear drift stochastic volatility model fits the international data well, I find that the level effect differs across countries.     

Further evidence on alternative continuous time models of the short-term interest rate

This paper examines the stochastic behavior of the 1-month interbank rate in ten countries. Various one-factor models are estimated using an exact maximum likelihood estimator, which is based on the recently introduced Gaussian methodology. Interest rate volatility is found to be less sensitive to interest rate levels than stated in the literature. In addition, the constant elasticity variance (CEV) model is superior to other formulations in terms of data fit.     

Long-memory and heterogeneous components in high frequency Pacific-Basin exchange rate volatility

Recent research examining high-frequency financial data has suggested that volatility dynamics may be confounded by the existence of an intra-day periodic pattern and multiple sources of volatility. This paper examines whether these dynamics are present in the US Dollar exchange rates of five Pacific Basin economies. Using 30-min sampled returns, evidence of a ‘U’-shape intra-day pattern in volatility for regional markets is reported and controlled for using a Flexible Fourier transform. Supportive evidence for the existence of multiple volatility components is offered by semi-parametric fractional difference estimates of the long-memory properties of absolute exchange rate returns at various intra-day data sampling frequencies. Further parametric evidence of an explicit component structure in such high frequency exchange rate volatility is offered by the estimates of a component-GARCH model which comprises both a long-run volatility component exhibiting slow shock decay and a short-run volatility component exhibiting far more rapid decay, and provides a generally superior fit to the data. Further application of these C-GARCH models in the analysis of high frequency volatility spillovers between the currencies considered also reveals that such spillovers are predominantly transitory rather than highly persistent in nature, but that where volatility spillovers do impact on the long-run component of exchange rate volatility the Australian Dollar plays a pivotal role in the localised causality transmission mechanism.      

Time-varying beta risk of Pan-European industry portfolios: A comparison of alternative modeling techniques

This paper investigates the time-varying behavior of systematic risk for 18 pan-European sectors. Using weekly data over the period 1987–2005, six different modeling techniques in addition to the standard constant coefficient model are employed: a bivariate t-GARCH(1,1) model, two Kalman filter (KF)-based approaches, a bivariate stochastic volatility model estimated via the efficient Monte Carlo likelihood technique as well as two Markov switching models. A comparison of ex-ante forecast performances of the different models indicate that the random walk process in connection with the KF is the preferred model to describe and forecast the time-varying behavior of sector betas in a European context.     

Bayesian range-based estimation of stochastic volatility models

Alizadeh, Brandt, and Diebold [2002. Journal of Finance 57, 1047–1091] propose estimating stochastic volatility models by quasi-maximum likelihood using data on the daily range of the log asset price process. We suggest a related Bayesian procedure that delivers exact likelihood based inferences. Our approach also incorporates data on the daily return and accommodates a nonzero drift. We illustrate through a Monte Carlo experiment that quasi-maximum likelihood using range data alone is remarkably close to exact likelihood based inferences using both range and return data.     

Time‐Varying Volatility in the Foreign Exchange Market: New Evidence on its Persistence and on Currency Spillovers

We examine empirically the volatility of four major US dollar spot exchange rates using intraday data over 40 trading days. Using multivariate stochastic volatility models, we investigate the degree of persistence of exchange rate volatility for data sampled at different frequencies and the role of volatility spillovers across exchange rates. We find that the noise component of volatility 'aggregates out' very quickly, being dominated by the more persistent component of volatility for data sampled at 15–minute or lower frequencies. Our results also suggest that exchange rate volatility is very persistent and that cross–currency spillovers are small.