Contrast estimation for noisy observations of diffusion processes via closed-form density expansions

When a continuous-time diffusion is observed only at discrete times with measurement noise, in most cases the transition density not known and likelihood form of high-dimensional integral that does have closed-form solution difficult to compute accurately. Using Hermite expansions deconvolution strategy, we provide general explicit sequence contrast for noisy discretely processes. This work allows estimation many We show approximation very accurate prove minimizing results consistent asymptotically normal estimator. Monte Carlo evidence Ornstein–Uhlenbeck process reveals this method works well outperforms Euler expansion situations relevant financial models.