Fulvio Pegoraro

Econometric Asset Pricing Modelling

The purpose of this paper is to propose a general econometric approach to no-arbitrage asset pricing modelling based on three main ingredients: (i) the historical discrete-time dynamics of the factor representing the information, (ii) the Stochastic Discount Factor (SDF), and (iii) the discrete-time risk-neutral (R.N.) factor dynamics. Retaining an exponential-affine specification of the SDF, its modelling is equivalent to the specification of the risk sensitivity vector and of the short rate, if the latter is neither exogenous nor a known function of the factor. In this general framework, we distinguish three modelling strategies: the Direct Modelling, the Risk-Neutral Constrained Direct Modelling and the Back Modelling. In all the approaches we study the Internal Consistency Conditions (ICCs), implied by the absence of arbitrage opportunity assumption, and the identification problem. The general modelling strategies are applied to two important domains: security market models and term structure of interest rates models. In these contexts we stress the usefulness (and we suggest the use) of the Risk-Neutral Constrained Direct Modelling and of the Back Modelling approaches, both allowing to conciliate a flexible (non-Car) historical dynamics and a Car R.N. dynamics leading to explicit or quasi explicit pricing formulas for various derivative products. Moreover, we highlight the possibility to specify asset pricing models able to accommodate non-Car historical and non-Car R.N. factor dynamics with tractable pricing formulas. This result is based on the notion of (Risk-Neutral) Extended Car process that we introduce in the paper, and which allows to deal with sophisticated models like Gaussian and Inverse Gaussian GARCH-type models with regime-switching, or Wishart Quadratic Term Structure models.

Pricing and Inference with Mixtures of Conditionally Normal Processes

We consider the problems of derivative pricing and inference when the stochastic discount factor has an exponential-affine form and the geometric return of the underlying asset has a dynamics characterized by a mixture of conditionally Normal processes. We consider both the static case in which the underlying process is a white noise distributed as a mixture of Gaussian distributions (including extreme risks and jump diffusions) and the dynamic case in which the underlying process is conditionally distributed as a mixture of Gaussian laws. Semi-parametric, non parametric and Switching Regime situations are also considered. In all cases, the risk-neutral processes and explicit pricing formulas are obtained.

Asset pricing with Second-Order Esscher Transforms

The purpose of the paper is to introduce, in a discrete-time no-arbitrage pricing context, a bridge between the historical and the risk-neutral state vector dynamics which is wider than the one implied by a classical exponential-affine stochastic discount factor (SDF) and to preserve, at the same time, the tractability and flexibility of the associated asset pricing model. This goal is achieved by introducing the notion of Exponential-Quadratic SDF or, equivalently, the notion of Second-Order Esscher Transform. The log-pricing kernel is specified as a quadratic function of the factor and the associated sources of risk are priced by means of possibly non-linear stochastic first-order and second-order risk-correction coefficients. Focusing on security market models, this approach is developed in the multivariate conditionally Gaussian framework and its usefulness is testified by the specification and calibration of what we name the Second-Order GARCH Option Pricing Model. The associated European Call option pricing formula generates a rich family of implied volatility smiles and skews able to match the typically observed ones.

Regime Switching and Bond Pricing

This article proposes an overview of the usefulness of the regime switching approach for building various kinds of bond pricing models and of the roles played by the regimes in these models. Both default-free and defaultable bonds are considered. The regimes can be used to capture stochastic drifts and/or volatilities, to represent discrete target rates, to incorporate business cycles or crises, to introduce contagion, to reproduce zero lower bound spells, or to evaluate the impact of standard or nonstandard monetary policies. From a technical point of view, we stress the key role of Markov chains, Compound Autoregressive (Car) processes, Regime Switching Car processes and multihorizon Laplace transforms.

Specification Analysis of International Treasury Yield Curve Factors

We show how to compute patterns of variation over time, both among and within countries, that determine the international term structure of interest rates, using maximum likelihood within a linear Gaussian state-space framework. The simultaneous estimation of common factors (shared by all countries) and local factors (specific to one country) requires development of a normalization procedure beyond that of ordinary factor analysis. By jointly estimating common and local factors we avoid sequential estimation effects that may explain the lack of agreement in the multi-country term structure literature regarding not only the total number of latent factors required to explain the joint dynamics of yield curves, but also the number of common and of local factors. Using data on international yield curves of U.S., Germany, U.K. and Japan from January 1986 to December 2009, we generally find (analyzing yields in level and in difference) that a model with two common factors and three correlated local factors is preferred to a model (of similar complexity) that includes one common factor only or a model with only correlated local factors. In addition, each common factor closely mimics (or is similar to) a local factor extracted from a pure local factor model. We also reach the conclusion that dependence across international yield curves are driven, first, by the instantaneous correlation between local factors of different countries and, then, by the (full) autoregressive matrix of latent factors and by the matrix of common loadings.

International Yield Curves and Principal Components Selection Techniques: An Empirical Assessment

Using a common database, we provide a controlled empirical comparison of recently-proposed principal component (PC) methods for selecting a combination of common and local factors that characterize the joint dynamics of multi-country term structures. We build a database of daily Treasury yield curves for U.S., Germany, U.K. and Japan, using common criteria to filter coupon bond data, to ensure liquidity, and to interpolate the discount function. We then estimate each proposed PC method for all subgroups of these countries, using both yield levels and yield differences at weekly frequency. We find, in general, that the proposed methods do not agree with one another on the preferred combination of common and/or local factors. We identify the explained variability decision criterion as an important source of this lack of agreement and recommend consideration of alternative statistical model selection techniques for the purpose of identifying common and local yield curve factors in international data.

Staying at Zero with Affine Processes: An Application to Term Structure Modelling

We build an Affine Term Structure Model that provides non-negative yields at any maturity and that is able to accommodate a short-term rate that stays at the zero lower bound (ZLB) for extended periods of time while longer-term rates feature high volatilities. We introduce these features through a new univariate non-negative affine process called ARG-Zero, and its multivariate affine counterpart (VARG), entailing conditional distributions with zero-point masses. The affine property of this new class of processes implies both explicit bond pricing and quasi-explicit lift-off probability formulas. We provide an empirical application to Japanese Government Bond (JGB) yields, observed weekly from June 1995 to May 2014 with maturities from six months to ten years. Our four-factor specification is able to closely match yield levels and to capture conditional yield variances.