Stochastic volatility

Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump-) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility models. For example, volatility is truly latent and this feature complicates estimation and inference. Further, the presence of an additional state variable - volatility - renders the model less tractable from an analytic perspective. We examine how such challenges have been addressed through development of new estimation methods and imposition of model restrictions allowing for closed-form solutions while remaining consistent with the dominant empirical features of the data.Stochastic analysis

Aspects of Credit Risk Modeling

Imperial Users onl

Precautionary saving and asset pricing: implications of separating time and risk preferences

It is a topic of active research in consumer and capital theory to determine how to characterize preferences about uncertainty and intertemporal choice. Intertemporal extensions of expected utility theory produce serious theoretical and empirical difficulties in many economic modeling applications by artificially restricting the functional forms used to characterize risk attitude and intertemporal preference. An important consequence is that these two distinct preference concepts become indistinguishable within an expected utility index. Recent theoretical work has produced alternatives to expected utility which allow independent specification of functional forms and thus permit the separation of the two preference parameters. This study uses a simple two-period labor-leisure and consumption model which can distinguish between an absolute risk aversion parameter and the elasticity of intertemporal substitution to show the asymmetric way each parameter influences intertemporal factor allocation decisions, particularly precautionary saving behavior, under alternative stochastic income sources. Pure endowment, pure capital return, and pure wage income risk, as well as various combinations of them, are all addressed in the study, and for each case a set of closed-form comparative static decision rules is derived. It is shown that intertemporal preference plays a significant role in determining factor supply decisions when either the intertemporal price of consumption or leisure is affected by risk, while risk attitude dominates behavior when intertemporal preferences are assumed homothetic and both intertemporal prices remain undisturbed. It is also shown that possible income correlation can magnify, dampen, or even reverse the comparative static implications in the three univariate cases. Computer simulations are used to derive numerical solutions for the model which highlight these effects;These results are contrasted with those obtained from an isoelastic expected utility model which entangles the risk attitude and intertemporal preference parameters, and thus treats each symmetrically in motivating factor allocation decisions over time;This study also examines the usefulness of a popular class of recursive preferences developed by Epstein and Zin (1989, 1991) for asset pricing applications. This class of preferences also distinguishes between risk attitude and intertemporal preference, and has been shown in the received literature to improve upon the poor empirical performance of expected utility in consumption-based models of asset pricing. However, using the nonparametric test procedure of Hansen and Jagannathan (1991) as well as seasonally unadjusted US data, it is shown in this study that little improvement occurs when moving from expected utility to this recursive class of preferences, suggesting that the meshing of preferences in the former does not account for its inability to explain the high volatility of asset prices in the US. Thus, while the added analytical power derived by independently specifying preference functional forms can generate new theoretical insights, this freedom may have limited usefulness in other areas of economic research

Linear state models for volatility estimation and prediction

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis concerns the calibration and estimation of linear state models for forecasting stock return volatility. In the first two chapters I present aspects of financial modelling theory and practice that are of particular relevance to the theme of this present work. In addition to this I review the literature concerning these aspects with a particular emphasis on the area of dynamic volatility models. These chapters set the scene and lay the foundations for subsequent empirical work and are a contribution in themselves. The structure of the models employed in the application chapters 4,5 and 6 is the state-space structure, or alternatively the models are known as unobserved components models. In the literature these models have been applied in the estimation of volatility, both for high frequency and low frequency data. As opposed to what has been carried out in the literature I propose the use of these models with Gaussian components. I suggest the implementation of these for high frequency data for short and medium term forecasting. I then demonstrate the calibration of these models and compare medium term forecasting performance for different forecasting methods and model variations as well as that of GARCH and constant volatility models. I then introduce implied volatility measurements leading to two-state models and verify whether this derivative-based information improves forecasting performance. In chapter 6I compare different unobserved components models' specification and forecasting performance. The appendices contain the extensive workings of the parameter estimates' standard error calculations

SEAM: A Small-Scale Euro Area Model With Forward-Looking Elements

This paper presents a small-scale estimated macro model for the euro area (SEAM) designed primarily to generate forecasts and to evaluate the dynamic response of the economy to unanticipated and anticipated shocks. One crucial feature of SEAM is the presence of forward-looking elements, which makes the model forecasts more robust to the 'Lucas critique', since it allows economic decisions to be moulded by the future impact of 'surprise' policy actions. In what concerns the reliability of the model-simulations, the inclusion of forward-looking behaviour enriches the dynamics of the response of the model's endogenous variables to exogenous shocks. Although the SEAM does not have the richness of full-scale macroeconometric models, as apparent interalia, by the absence of a steady-state analogue and also of some relationships important for a better characterisation of the euro area economy, the model has been shown to deliver reasonable forecasts and responses to shocks that are consistent with conventional wisdom.

Generalized single-index models: The EFM approach

Generalized single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and finan- cial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, beta = 1, represents a non-regular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM ap- proach, a method of estimating functions, to study the generalized single-index model. The procedure is to first relax the equality constraint to one with (d - 1) components of beta lying in an open unit ball, and then to construct the associated (d - 1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the re- sulting estimating equations is achieved, and a Wilk's type theorem for testing the index is demonstrated. A noticeable result we obtain is that our estimator for beta has smaller or equal limiting variance than the estimator of Carroll et al. (1997). A fixed point iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Numerical studies based on simulation and on applications suggest that this new estimating system is quite powerful and easy to implement.Generalized single-index model, index coefficients, estimating equations, asymptotic properties, iteration

"Rotterdam econometrics": publications of the econometric institute 1956-2005

This paper contains a list of all publications over the period 1956-2005, as reported in the Rotterdam Econometric Institute Reprint series during 1957-2005.

Inference in a Synchronization Game with Social Interactions, Second Version

This paper studies inference in a continuous time game where an agent's decision to quit an activity depends on the participation of other players. In equilibrium, similar actions can be explained not only by direct influences but also by correlated factors. Our model can be seen as a simultaneous duration model with multiple decision makers and interdependent durations. We study the problem of determining the existence and uniqueness of equilibrium stopping strategies in this setting. This paper provides results and conditions for the detection of these endogenous effects. First, we show that the presence of such effects is a necessary and sufficient condition for simultaneous exits. This allows us to set up a nonparametric test for the presence of such influences which is robust to multiple equilibria. Second, we provide conditions under which parameters in the game are identified. Finally, we apply the model to data on desertion in the Union Army during the American Civil War and find evidence of endogenous influences.duration models, social interactions, empirical games, optimal stopping