Class EuropeanOptionSmileByCarrMadan

All Implemented Interfaces:
Function<org.apache.commons.math3.complex.Complex,org.apache.commons.math3.complex.Complex>, CharacteristicFunction, SmileByIntegralTransform

public class EuropeanOptionSmileByCarrMadan extends EuropeanOptionSmile
This class computes the prices of a collection of call options for a fixed maturity and a family of strikes. The pricing method is the FFT methodology as introduced in Carr and Madan (1999). The transform is taken for -1 < \alpha < 0, hence we have a correction term since we are applying the residue theorem as reported in Lee (2004). In this strip the transform of any meaningful financial model is well defined because we expect the following conditions to be satisfied: 1) When computed in the point z=-i, the discounted characteristic function gives us the initial asset price due to the martingale property. 2) By definition of characteristic function also z = 0 is a good point. Analytic extension over the strip is then guaranteed by Lukacs (1970), Theorem 7.1.1. From a financial point of view the choice of this strip corresponds to transforming a covered call position. References:
  • Carr. P. and Madan, D. (1999) Option Valuation Using the Fast Fourier Transform. Journal of Computational Finance.
  • Lee, R. (2004) Option pricing by transform methods: extensions, unification and error control. Journal of Computational Finance.
  • Lewis, A. (2002) A simple option formula for general jump diffusion and other exponential Levy processes.
  • Lukacks, E. (1970) Characteristic Functions. 2nd edition.
Alessandro Gnoatto