In financial mathematics, the Carr–Madan formula of Peter Carr and Dilip B. Madan shows that the analytical solution of the European option price can be obtained once the explicit form of the characteristic function of \( {\displaystyle \log S_{t}} \), where \( S_{t} \) is the price of the underlying asset at time t, is available.[1] This analytical solution is in the form of the Fourier transform, which then allows for the fast Fourier transform to be employed to numerically compute option values and Greeks in an efficient manner.
References
Carr, Peter; Madan, Dilip B. (1999). "Option valuation using the fast Fourier transform". Journal of Computational Finance. 2 (4): 61–73. CiteSeerX 10.1.1.348.4044. doi:10.21314/JCF.1999.043.
Further reading
Crépey, Stéphane (2013), "5.5.3 Carr–Madan Formula", Financial Modeling: A Backward Stochastic Differential Equations Perspective, Springer, pp. 153–155, ISBN 9783642371134.
Hirsa, Ali (2013), Computational Methods in Finance, Chapman and Hall/CRC Financial Mathematics Series, CRC Press, pp. 1–82, ISBN 9781439829578
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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