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## MCMC Analysis of Diffusion Models with Application to Finance (1998)

Venue: | Journal of Business and Economic Statistics |

Citations: | 143 - 4 self |

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Citation Context ...th, Teller, and Teller 1953) was successfully applied to one-factor models for the interest rate. Still, we suggest using the hybrid accept/reject Metropolis Hastings (hereafter AR-MH) algorithm (see =-=Tierney 1994-=-) to be discussed below, as this algorithm appears to give more rapid convergence. The AR-MH algorithm is very general and only requires knowledge of the unnormalized target density (here: p) and a pr... |

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Citation Context ...for estimating diffusions by the method of simulated moments (Duffie and Singleton 1993), indirect inference methods (Gourieroux, Monfort, and Renault 1993) and the efficient method of moments (EMM) (=-=Gallant and Tauchen 1996-=-) among others. The advantage of simulation based methods is that they typically apply to more general processes than the analytic methods. For instance, Andersen and Lund (1997a,b) apply EMM in estim... |

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Citation Context ...second step. By repeating this process, the sequence of simulated parameters and missing data forms a Markov chain for which the stationary distribution is the posterior distribution of interest (see =-=Casella and George 1992-=-, and Albert and Chib 1996 for discussions) . 2.2 Conditional Posterior for Missing Data Unfortunately, sampling all the missing observations in one operation is impossible due to high dimensionality ... |

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Citation Context ...n proposed in Ait-Sahalia (1996a,b), Jiang and Knight (1997), and Stanton (1997). Previously, simulation-based methods have been proposed for estimating diffusions by the method of simulated moments (=-=Duffie and Singleton 1993-=-), indirect inference methods (Gourieroux, Monfort, and Renault 1993) and the efficient method of moments (EMM) (Gallant and Tauchen 1996) among others. The advantage of simulation based methods is th... |

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Citation Context ...pecification does not fully capture the dynamics in the interest rates. Alternative drift specifications such as the non-linear one in Ait-Sahalia (1996b) and the central tendency factor model (e.g., =-=Andersen and Lund 1997-=-b) could potentially capture this model departure. Yet, the inability of the CEV model to fit the conditional mean dynamics of the interest rate process is not the only evidence of mis-specification: ... |

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Citation Context ...etization becomes finer and as the dimensionality, d, of the system increases. Most noticeably however, unconditional simulation is typically inadequate for handling models with latent variables (see =-=Danielsson 1994-=- for a discussion of this in the context of discrete SV models). The next step in setting up a Gibbs sampler for this problem is to devise some method to simulatesY i j Y i\Gamma1 ; Y i+1 ; `. We star... |

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Citation Context ...o be advantageous to that of asymptotic approximations. Although we are primarily concerned with Bayesian calculations here, MCMC simulations can also be used for maximum likelihood estimation (e.g., =-=Geyer 1996-=-). Finally, though not pursued in detail, the principles outlined here allow estimation of multivariate models in which variables are sampled at different times and possibly non-synchronously. This of... |

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(Show Context)
Citation Context ...pecification does not fully capture the dynamics in the interest rates. Alternative drift specifications such as the non-linear one in Ait-Sahalia (1996b) and the central tendency factor model (e.g., =-=Andersen and Lund 1997-=-b) could potentially capture this model departure. Yet, the inability of the CEV model to fit the conditional mean dynamics of the interest rate process is not the only evidence of mis-specification: ... |

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Citation Context ... t = 0; 1; 2; ::; T , j = 1; 2; ::; d 1 to be used in estimation where d 1sd. A1 is sufficient to ensure the existence of a strong (unique), square integrable solution Y t ; t 2 [0; T ] to (1) (e.g., =-=ksendal 1995-=-, p. 64). More importantly, bounded growth of the diffusion function is required for the key step in the MCMC sampling algorithm. We elaborate on this below. It is sufficient that the conditions hold ... |

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Citation Context ...s process, the sequence of simulated parameters and missing data forms a Markov chain for which the stationary distribution is the posterior distribution of interest (see Casella and George 1992, and =-=Albert and Chib 1996-=- for discussions) . 2.2 Conditional Posterior for Missing Data Unfortunately, sampling all the missing observations in one operation is impossible due to high dimensionality of the associated density.... |

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