On the data-driven COS method

Journal article (2018)

Authors

A. Leitao Rodriguez Numerical Analysis - , Centrum Wiskunde & Informatica (CWI)

C.W. Oosterlee Centrum Wiskunde & Informatica (CWI), Numerical Analysis -

Luis Ortiz-Gracia Universitat Politecnica de Catalunya

SM Bohte Centrum Wiskunde & Informatica (CWI)

Research Group

Numerical Analysis () (TU Delft)

Greeks Density estimation Data-driven approach Delta–Gamma approach The COS method The SABR model

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Published Date

2018

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

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 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 methods 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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