Discretely Observed Diffusions: Approximation of the Continuous-time Score Function

Discretely Observed Diffusions: Approximation of the Continuous-time Score Function

Quasi-maximum Likelihood Estimation of Discretely Observed Diffusions∗

This paper introduces quasi-maximum likelihood estimator for discretely observed diffusions when a closed-form transition density is unavailable. Higher order Wagner-Platen strong approximation is used to derive the first two conditional moments and a normal density function is used in estimation. Simulation study shows that the proposed estimator has high numerical precision and good numerical...

Maximum Likelihood Estimation of Discretely Sampled Diffusions: a Closed-form Approximation Approach

When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very a...

Retrospective Exact Simulation of Diffusion Sample Paths with Applications

The objective of this paper is to present an algorithm, for exact simulation of a class of Ito’s diffusions. We demonstrate that when the algorithm is applicable, it is also straightforward to simulate diffusions conditioned to hit specific values at predetermined time instances. We also describe a method that exploits the properties of the algorithm to carry out inference on discretely observe...

Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach

This paper develops an eigenfunction expansion approach to solve discretely monitored first passage time problems for a rich class of Markov processes, including diffusions and subordinate diffusions with jumps, whose transition or Feynman-Kac semigroups possess eigenfunction expansions in L spaces. Many processes important in finance are in this class, including OU, CIR, (JD)CEV diffusions and...