Sergio Pastorello

Statistical Inference for Random-Variance Option Pricing

This article deals with the estimation of continuous-time stochastic volatility models of option pricing. We argue that option prices are much more informative about the parameters than are asset prices. This is confirmed in a Monte Carlo experiment that compares two very simple strategies based on the different information sets. Both approaches are based on indirect inference and avoid any discretization bias by simulating the continuous-time model. We assume an Ornstein-Uhlenbeck process for the log of the volatility, a zero-volatility risk premium, and no leverage effect. We do not pursue asymptotic efficiency or specification issues; rather, we stick to a framework with no overidentifying restrictions and show that, given our option-pricing model, estimation based on option prices is much more precise in samples of typical size, without increasing the computational burden.

Modelling the demand for M3 in the Euro area

Modelling monetary transmission is central to understanding the role of monetary policy in the Euro area, and money demand is commonly seen as a link in that transmission mechanism. Since the beginning of the 1990s, many studies have suggested that the demand for Euro area broad money is stable over the long run because the estimation of an area-wide demand for money function provides an appropriate solution to a number of potential causes of misspecification of the single-country relations (such as spillover effects and currency substitution), and enjoys the positive consequences of a statistical averaging effect. On the other side, it must be stressed that previous benefits can be achieved at the risk of introducing parameter heterogeneity into the area-wide relationship. In order to shed some light on the issue, this study is first devoted to an analysis of the main econometric features of the money M3 demand at Euro area and single country levels, then it compares the two sets of results in a common framework that, differently from all previous studies, explicitly takes account of the potential nonstationarity of the variables of interest in both estimation and testing phases. The comparison shows that the area-wide money demand is more smooth and less subject to shocks than the single-country ones. Finally, a number of poolability tests run over subgroups highlight that low precision associated with the estimates of the parameters of the national models makes it impossible to exclude that their long-run specifications do in fact coincide.

Iterative and Recursive Estimation in Structural Nonadaptive Models

An inference method, called latent backfitting, is proposed. This method appears well suited for econometric models where the structural relationships of interest define the observed endogenous variables as a known function of unobserved state variables and unknown parameters. This nonlinear state-space specification paves the way for iterative or recursive EM-like strategies. In the E steps, the state variables are forecasted given the observations and a value of the parameters. In the M steps, these forecasts are used to deduce estimators of the unknown parameters from the statistical model of latent variables. The proposed iterative/recursive estimation is particularly useful for latent regression models and for dynamic equilibrium models involving latent state variables. Practical implementation issues are discussed through the example of term structure models of interest rates.

Maximization by Parts in Extremum Estimation

In this paper, we present various iterative algorithms for extremum estimation in cases where direct computation of the extremum estimator or via the Newton–Raphson algorithm is difficult, if not impossible. While the Newton–Raphson algorithm makes use of the full Hessian matrix, which may be difficult to evaluate, our algorithms use parts of the Hessian matrix only, the parts that are easier to compute. We establish consistency and asymptotic efficiency of our iterative estimators under regularity and information dominance conditions. We argue that the economic interpretation of a structural econometric model will often allow us to give credibility to a well‐suited information dominance condition. We apply our algorithms to the estimation of the Merton structural credit risk model and to the Heston stochastic volatility option pricing model.

Efficient importance sampling maximum likelihood estimation of stochastic differential equations

Maximum likelihood estimation (MLE) of stochastic differential equations (SDEs) is difficult because in general the transition density function of these processes is not known in closed form, and has to be approximated somehow. An approximation based on efficient importance sampling (EIS) is detailed. Monte Carlo experiments, based on widely used diffusion processes, evaluate its performance against an alternative importance sampling (IS) strategy, showing that EIS is at least equivalent, if not superior, while allowing a greater flexibility needed when examining more complicated models.

European Spreads at the Interest Rate Lower Bound

This paper analyzes the effect of the interest rate lower bound on long term sovereign bond spreads in the Euro area. We specify a joint shadow rate term structure model for the risk-free, the German and the Italian sovereign yield curves. In our model, the behavior of long term spreads becomes strongly nonlinear in the underlying factors when interest rates are close to the lower bound, which in the data occurs since the beginning of 2012. We fit the model by Quasi-Maximum Likelihood and highlight three important consequences of sovereign spreads’ nonlinear behavior: i) their distribution is skewed, ii) they are affected by (possibly exogenous) changes in the lower bound, and iii) they become less informative about the countries’ sovereign risk. Shadow spreads, however, still provide reliable information.