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Quantitative Finance · Glossary

What is Lewis formula?

Definition 24.1 Derivatives and Volatility · Chapter 24 — Fourier Pricing and Calibration Engineering

The Lewis formula prices a European call from the characteristic function of xTx_T along the line Im⁡u=−12\operatorname{Im}u=-\frac12: with k=ln⁡(K/F)k=\ln(K/F),

C=P(0,T)(F−FKπ∫0∞Re⁡(e−iukφ(u−i2))duu2+14).C=P(0,T)\Bigl(F-\frac{\sqrt{FK}}{\pi}\int_0^\infty\operatorname{Re}\bigl(e^{-iuk}\varphi(u-\tfrac i2)\bigr)\frac{du}{u^2+\frac14}\Bigr).
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