MCMC Analysis of Diffusion Models With Application to Finance

By Bjørn Eraker. 2001

486 citations recorded by the source corpus.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3aedaddb68a2f43e8691876b25d707c90acb8f75

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Citations in the corpus

CHAPTER 4 – Estimating Functions for Discretely Sampled Diffusion-Type Models (2010, methodology): “Bayesian estimators with the same asymptotic properties as the maximum likelihood estimator can be obtained by Markov chain Monte Carlo methods, see Elerian, Chib & Shephard (2001), Eraker (2001) , Roberts & Stramer (2001), and Johannes & Polson (2003).”
Simulation Methods for Lévy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models (2006, background): “With exceptions (e.g., Eraker 2001; Elerian, Chib, and Shephard 2001), MCMC applications typically assume that the sampling interval is the same as a tick on the continuous-time clock, which greatly reduces the number of unobserved variables that must be dealt with.”
Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed‐form Approximation Approach (2002, background): “For instance, they could be used for derivative pricing, for indirect inference (see Gouriéroux, Monfort, and Renault (1993)), which in its simplest version uses an Euler approximation as instrumental model, or for Bayesian inference—basically whenever an expression for the transition density is req”
Markov Chain Monte Carlo Data Association for Multi-Target Tracking (2009, background): “Markov chain Monte Carlo (MCMC) plays a significant role in many fields such as physics, statistics, economics, finance, and engineering [28]–[30].”
Bayesian forecasting in economics and finance: A modern review (2022, methodology): “Estimation of and forecasting with such models is nevertheless computationally feasible via Bayesian methods, with MCMC algorithms of one form or another forming the backbone of the early treatments (Eraker, 2001; Eraker et al., 2003; Eraker, 2004; Forbes et al., 2007; Johannes et al., 2009).”
Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations (2006, methodology): “Bayesian analysis of discretely observed SDEs has been studied independently by Elerian, Chib and Shephard (2001), Eraker (2001), Roberts and Stramer (2001) and Jones (1998).”
Estimating the Parameters of Stochastic Volatility Models Using Option Price Data (2015, methodology): “Eraker (2004) uses a sampling strategy in which a contract that trades on the first day of the sample is chosen at random.”
Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility (2004, background): “The results of Jones (2003b) and Eraker (2001) suggest that even nonlinear term structure models do not suffer from appreciable discretization bias when the discretization interval is set equal to one day.”
Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey (2004, methodology): “Also, it applies to models that are only partially observed (e.g. stochastic volatility models) in which case the values of the unobserved coordinates are simulated like X̃ above (Eraker, 2001).”
Statistical Methods for Stochastic Differential Equations (2012, methodology): “Asymptotic results for the maximum likelihood estimator in the low frequency (fixed ∆) asymptotic scenario considered in that subsection were established by Dacunha-Castelle & Florens-Zmirou (1986). Asymptotic results when the observations are made at random time points were obtained by Aı̈t-Sahalia”
The dynamics of stochastic volatility: evidence from underlying and options markets (2003, methodology): “As in Eraker ( 2001 ) , model diagnostics may be developed by examining the residuals deÿned implicitly by the Euler approximation of the SDE .”
Stochastic volatility with leverage: Fast and efficient likelihood inference (2007, methodology): “Thus, the methods we develop in this paper, combined with those of Elerian et al. (2001), Eraker (2001) and Roberts and Stramer (2001), can be used to fit the corresponding continuous time model with discretely sampled data.”