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Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C.B. Phillips, Jun Yu
Maximum Likelihood And Gaussian Estimation Of Continuous Time Models In Finance, Peter C.B. Phillips, Jun Yu
Cowles Foundation Discussion Papers
This paper overviews maximum likelihood and Gaussian methods of estimating continuous time models used in finance. Since the exact likelihood can be constructed only in special cases, much attention has been devoted to the development of methods designed to approximate the likelihood. These approaches range from crude Euler-type approximations and higher order stochastic Taylor series expansions to more complex polynomial-based expansions and infill approximations to the likelihood based on a continuous time data record. The methods are discussed, their properties are outlined and their relative finite sample performance compared in a simulation experiment with the nonlinear CIR diffusion model, which …
Simulation-Based Estimation Of Contingent-Claims Prices, Peter C.B. Phillips, Jun Yu
Simulation-Based Estimation Of Contingent-Claims Prices, Peter C.B. Phillips, Jun Yu
Cowles Foundation Discussion Papers
A new methodology is proposed to estimate theoretical prices of financial contingent-claims whose values are dependent on some other underlying financial assets. In the literature the preferred choice of estimator is usually maximum likelihood (ML). ML has strong asymptotic justification but is not necessarily the best method in finite samples. The present paper proposes instead a simulation-based method that improves the finite sample performance of the ML estimator while maintaining its good asymptotic properties. The methods are implemented and evaluated here in the Black-Scholes option pricing model and in the Vasicek bond pricing model, but have wider applicability. Monte Carlo …