By Yacine Ait-Sahalia, Lars Peter Hansen
Utilized monetary econometrics matters are featured during this moment quantity, with papers that survey very important study whilst they make specified empirical contributions to the literature. those matters are typical: portfolio selection, buying and selling quantity, the risk-return tradeoff, choice pricing, bond yields, and the administration, supervision, and size of utmost and rare dangers. but their remedies are unheard of, drawing on present facts and facts to mirror contemporary occasions and scholarship. A landmark in its insurance, this quantity may still propel monetary econometric learn for years. provides a large survey of present researchContributors are prime econometriciansOffers a readability of technique and clarification unavailable in different monetary econometrics collections
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Additional info for Handbook of Financial Econometrics, Volume 2: Applications (Handbooks in Finance)
Section 5 provides a tutorial on MCMC methods, building algorithms for equity price, option price, term structure, and regime switching models. Section 6 concludes and provides directions for future research. 2. OVERVIEW OF BAYESIAN INFERENCE AND MCMC This section provides a brief, nontechnical overview of MCMC and Bayesian methods. We ﬁrst describe the mechanics of MCMC simulation, and then we show how to use MCMC methods to compute objects of interest in Bayesian inference. 1. MCMC Simulation and Estimation MCMC generates random samples from a given target distribution, in our case, the distribution of parameters and state variables given the observed prices, p( , X |Y ).
To generate samples from π( ), a Metropolis–Hastings algorithm requires the researcher to specify a recognizable proposal or candidate density q (g+1) | (g ) . In most cases this distribution will depend critically on the other parameters, the state variables and the previous draws for the parameter being drawn. As in Metropolis et al. (1953), we only require that we can evaluate density ratio π (g+1) /π (g) easily. This is a mild assumption, which is satisﬁed in all of the continuous-time models that we consider.
Hobert and Casella (1996) provide a number of general examples. For example, in a logstochastic volatility, a “noninformative” prior on σv of p(σv ) ∝ σv−1 results in a proper conditional posterior for σv but an improper joint posterior that leads to a degenerate MCMC algorithm. In some cases, the propriety of the joint posterior cannot be checked analytically, and in this case, simulation studies can be reassuring. We recommend using proper priors always be used unless there is a very strong justiﬁcation for doing otherwise.