Abstract

One of the numerically preferred methods for fitting a function to noisy data when the underlying function is known to be smooth is to minimize the roughness of the fit while placing a limit on the sum of squared errors. We show that the fit can be formulated as a solution to a convex program. Since convex programs can be solved by various methods with guaranteed convergence, our formulation enables one to use these methods to compute the fit numerically. Numerical results show that our formulation is successfully applied to the problem of sensitivity estimation of option prices as functions of the underlying stock price.

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