In this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based finan- cial option valuation method which assumes the availability of asset data samples: a char- acteristic function of the underlying asset probability density function is not required. As such, the presented technique represents a generalization of the well-known COS method [1]. The convergence of the proposed method is O(1 / √ n ) , in line with Monte Carlo meth- ods for pricing financial derivatives. The ddCOS method is then 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.

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Applied Mathematics and Computation
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Leitao Rodriguez, Á, Oosterlee, C.W, Ortiz Gracia, L, & Bohte, S.M. (2018). On the data-driven COS method. Applied Mathematics and Computation, 317, 68–84. doi:10.1016/j.amc.2017.09.002