  The accuracy of least squares calibration using option premiums and particle
filtering of price data to find model parameters is determined. Derivative
models using exponential L\'evy processes are calibrated using regularized
weighted least squares with respect to the minimal entropy martingale measure.
Sequential importance resampling is used for the Bayesian inference problem of
time series parameter estimation with proposal distribution determined using
extended Kalman filter. The algorithms converge to their respective global
optima using a highly parallelizable statistical optimization approach using a
grid of initial positions. Each of these methods should produce the same
parameters. We investigate this assertion.
