In financial mathematics, the Carr–Madan formula of Peter Carr and Dilip B. Madan^[1] 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 ${\displaystyle S_{t}}$ is the price of the underlying asset at time ${\displaystyle t}$, is available.^[2] 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

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