Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
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For some popular financial continuous-time models, tractable expressions of likelihood functions are unknown. For that reason, the maximum likelihood estimation method is infeasible. Fortunately, closed functional forms of conditional characteristic functions of some of these models are known. We construct an empirical likelihood estimation method using tractable conditional characteristic functions to estimate such a model. This method resolves the problem of covariance matrix singularity in the standard generalized method of moments and fully utilizes information in conditional moment restrictions. It is applicable to many popular financial models such as some diffusion models, jump diffusion models, and stochastic volatility models. Using a Monte Carlo comparison, we show that this method provides superior performance compared to other methods in some situations.