A Conversation with Eric Ghysels

Published in Econometric Theory, 2012, https://doi.org/10.1017/S026646661100017X</p

Dating the Timeline of Financial Bubbles during the Subprime Crisis

A new recursive regression methodology is introduced to analyze the bubble characteristics of various financial time series during the subprime crisis. The methods modify a technique proposed in Phillips, Wu and Yu (2010) and provide a technology for identifying bubble behavior and consistent dating of their origination and collapse. The tests also serve as an early warning diagnostic of bubble activity. Seven relevant financial series are investigated, including three financial assets (the Nasdaq index, home price index and asset-backed commercial paper), two commodities (the crude oil price and platinum price), one bond rate (Baa), and one exchange rate (Pound/USD). Statistically significant bubble characteristics are found in all of these series. The empirical estimates of the origination and collapse dates suggest an interesting migration mechanism among the financial variables: a bubble first emerged in the equity market during mid-1995 lasting to the end of 2000, followed by a bubble in the real estate market between January 2001 and July 2007 and in the mortgage market between November 2005 and August 2007. After the subprime crisis erupted, the phenomenon migrated selectively into the commodity market and the foreign exchange market, creating bubbles which subsequently burst at the end of 2008, just as the effects on the real economy and economic growth became manifest. Our empirical estimates of the origination and collapse dates match well with the general datetimes of this crisis put forward in a recent study by Caballero, Farhi and Gourinchas (2008).Financial bubbles, Crashes, Date stamping, Explosive behavior, Mildly explosive process, Subprime crisis, Timeline

A Two-Stage Realized Volatility Approach to Estimation of Diffusion Processes with Discrete

This paper motivates and introduces a two-stage method of estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as developed in Jacod (1994) and Barndorff-Nielsen and Shephard (2002), to provide a regression model for estimating the parameters in the diffusion function. In the second stage the in-fill likelihood function is derived by means of the Girsanov theorem and then used to estimate the parameters in the drift function. Consistency and asymptotic distribution theory for these estimates are established in various contexts. The finite sample performance of the proposed method is compared with that of the approximate maximum likelihood method of At-Sahalia (2002).Maximum likelihood, Girsnov theorem, Discrete sampling, Continuous record, realized volatility

Simulation-based Estimation of Contingent-claims Prices

A new methodology is proposed to estimate theortical prices of financial contingent-claims whose values are dependent on some other underlying financial assets. In the literature the preferred choice of estimator is usually maximum likelihood (ML). ML has strong asymptotic justification but is not necessarily the best method in finite samples. The present paper proposes instead a simulation-based method that improves the finite sample performance of the ML estimator while maintaining its good asymptotic properties. The methods are implemented and evaluated here in the Black-Scholes option pricing model and in the Vasicek bond pricing model, but have wider applicability. Monte Carlo studies show that the proposed procedures achieve bias reductions overML estimation in pricing contingent claims. The bias reductions are sometimes accompanied by reductions in variance, leading to significant overall gains in mean squared estimation error. Empirical applications to US treasure bills highlight the differences between the bond prices implied by the simulation-based approach and those delivered by ML and the consequences on the statistical tesing of contingent-claim pricing models.Bias Reduction, Bond Pricing, Indirect Inference, Option Pricing, Simulation-based Estimation

Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance

This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These approaches range from crude Euler-type approximations and higher order stochastic Taylor series expansions to more complex polynomial-based expansions and infill approximations to the likelihood based on a continuous time data record. The methods are discussed, their properties are outlined and their relative finite sample performance compared in a simulation experiment with the nonlinear CIR diffusion model, which is popular in empirical finance. Bias correction methods are also considered and particular attention is given to jackknife and indirect inference estimators. The latter retains the good asymptotic properties of ML estimation while removing finite sample bias. This method demonstrates superior performance in finite samples.Maximum likelihood, Transition density, Discrete sampling, Continuous record, realized volatility, Bias Reduction, Jackknife, Indirect Inference

Comments on “A Selective Overview of Nonparametric Methods in Financial Econometrics” by Jianqing Fan

Our comments on Fan’s paper will concentrate on two issues that relate in important ways to the paper’s focus on misspecification and discretization bias and the role of nonparametric methods in empirical finance.