On the Data-Driven COS Method
Applied Mathematics and Computation 317: 68-84, 2018
26 Pages Posted: 16 Feb 2017 Last revised: 28 Oct 2018
Date Written: February 15, 2017
In this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based financial option valuation method which assumes the availability of asset data samples: a characteristic function of the underlying asset probability density function is not required. As such, the method represents a generalization of the well-known COS method. Convergence with respect to the number of asset samples is according the convergence of Monte Carlo methods for pricing financial derivatives. The ddCOS method is particularly interesting for density recovery and also for the efficient computation of the option’s sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods.
Keywords: Fourier, Density estimation, Statistical Learning theory, Greeks
JEL Classification: C16; C63
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