Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes

By Garland B. Durham, Ronald Gallant. 2002

489 citations recorded by the source corpus.

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Citations in the corpus

Impact of jumps on returns and realised variances: econometric analysis of time-deformed Lévy processes (2006, methodology): “…(1998)), (ii) simulation based indirect inference (e.g. Gourieroux, Monfort, and Renault (1993), Gallant and Tauchen (1996)), (iii) generalised method of moments (e.g. Andersen and Sorensen (1996)), (iv) simulation based maximum likelihood using important sampling (e.g. Durham and Gallant (2002)).”
Jackknifing Bond Option Prices (2005, unknown): “Examples include simulated GMM [Duffie and Singleton (1993)] and its refinement EMM [Gallant and Tauchen (1996)], indirect inference [Gourieroux, Monfort and Renault (1993)], continuous time GMM [Hansen and Scheikman (1995)], approximate ML [Ao¨t-Sahalia (2002, 2003), Duffie, Pedersen, and Singleton”
Simulation Methods for Lévy-Driven Continuous-Time Autoregressive Moving Average (CARMA) Stochastic Volatility Models (2006, methodology): “Simulated likelihood in the manner of Durham and Gallant (2002) is applicable only in certain cases, because the joint density of the observed and unobserved variables is generally not available, and so there is no convenient way to define an importance function for efficient simulation.”
Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models (2006, methodology): “…W 1 and W 2 are (possibly correlated) Brownian motions, use Ito’s rule with pffiffiffiffiffi the transformation ht ¼ Vt to get dY t ¼ m dt þ ht dW 1t ( ) f s2 s dht ¼ a - - h2 dt þ dW 2t.t2ht 4f 2 This is the same ‘‘volatility-stabilizing transformation’’ used in Durham and Gallant (2002).”
Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes (2009, unknown): “Also, approximate Monte Carlo maximum likelihood approaches have been suggested, most notably by [32] and [16].”
Bayesian inference for irreducible diffusion processes using the pseudo-marginal approach (2011, methodology): “The integral in (4) is evaluated in Durham and Gallant (2002) using importance sampling: p(M)(∆, xi+1|xi, θ) = Eq[RM (U)] (5) where U = (U1, .”
Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance (2007, methodology): “As noted in Durham and Gallant (2002), there are two sources of approximation error in Pedersens method. One is the (albeit reduced) discretization bias in the Euler scheme. The second is due to the Monte Carlo integration. These two errors can be further reduced by increasing the number of latent ”
Affine Term Structure Models (2010, unknown): “For example, the short rate is quadratic in Constantinides (1992), El Karoui et al. (1993), and Ahn et al.”
A Gaussian approach for continuous time models of the short-term interest rate (2001, background): “Duffie and Singleton (1993), Gallant and Tauchen (1996), Eraker (2001), Elerian et al. (2001), Durham and Gallant (2002) ), some are based on numerical approximations (such as Lo (1988)), while others are based on closed-form approximations (such as A¨ it-Sahalia (1999, 2000)).”
Exact and computationally efficient likelihood‐based estimation for discretely observed diffusion processes (with discussion) (2006, methodology): “The simulation approach is in general more amenable when this transformation can be done (see Durham and Gallant (2002)).”
Testing the assumptions behind importance sampling (2009, methodology): “R I This is the case in the stochastic volatility literature; see, e.g., Hendry and Richard (1991), Danielsson and Richard (1993), Sandmann and Koopman (1998), Elerian, Chib, and Shephard (2001), Durham and Gallant (2002), Durham (2006), and Asai and McAleer (2006).”
Monte Carlo State-Space Likelihoods by Weighted Posterior Kernel Density Estimation (2004, methodology): “MC state-space research has typically considered methods for single long time series, such as for nancial data (Carlin, Polson, and Stoffer 1992; Shephard and Pitt 1997; Tanizaki and Mariano 1998; Pitt and Shephard 1999; Durham and Gallant 2002) or sheries catch and survey records (Bjørnstad, Fr”
A Simple Approach to the Parametric Estimation of Potentially Nonstationary Diffusions (2005, background): “For example, Brandt and Santa-Clara (2002), Durham and Gallant (2002), Elerian et al. (2001) and Eraker (2001) among others, suggest simulation-based procedures for maximum likelihood estimation.”
Maximum Likelihood Estimation of Latent Affine Processes (2006, unknown): “…Alternatively, the log densities may be evaluated numerically: by Fourier inversion of the conditional characteristic function, by numerical finite-difference methods (Lo, 1988), by simulation methods (e.g., Durham and Gallant, 2002), or by good approximation techniques (Aït-Sahalia, 2002).”
Leverage and Volatility Feedback Effects in High-Frequency Data (2006, methodology): “To enhance the numerical stability, we simulate the square root of the volatility process, Zt = √ Vt, which by Ito’s Lemma has a constant diffusion term, dZt = − β 2Zt ( −α β + σ2 2β − Z2t ) dt+ 1 2 σdWt, see Durham and Gallant (2002) for further discussion along these lines.”
CHAPTER 4 – Estimating Functions for Discretely Sampled Diffusion-Type Models (2010, unknown): “There are a number approaches that render likelihood inference and Bayesian inference feasible for ordinary diffusion models; for likelihood inference, see Pedersen (1995), Poulsen (1999), A¨ot-Sahalia (2002), Durham & Gallant (2002) , and A¨ot-Sahalia, Hansen & Scheinkman (2003), and for Markov ch”