SUMMARY .................................................................................................................................. 4

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Different continuous-time models for interest rates coexist in the literature. We test parametric models by comparing their implied parametric density to the same density estimated nonparametrically. We do not replace the continuous-time model by discrete approximations, even though the data are recorded at discrete intervals. The principal source of rejection of existing models is the strong nonlinearity of the drift. Around its mean, where the drift is essentially zero, the spot rate behaves like a random walk. The drift then mean-reverts strongly when far away from the mean. The volatility is higher when away from the mean.

Testing Continuous-Time Models of the Spot Interest Rate

Using the wavelet-Galerkin method for solving partial integro-differential equations, we derive an implement computationally efficient formula for pricing European options on assets driven by multivariate jump-diffusions. This pricing formula is then used to solve the inverse problem of estimating the corresponding risk-neutral coefficient functions of the underlying jump-diffusions from observed option data. The ill-posedness of this estimation problem is proved, and a consistent estimation technique employing Tikhonov regularization is proposed. Using S&P 500 Index option data, it is shown that the coefficient functions in a stochastic volatility model with jumps are nonlinear, contrary to the affine specification widely used in the literature.

Recovering Nonlinear Dynamics from Option Prices

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Recovering Nonlinear Dynamics from Option Prices