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The Carr-Madan Fast Fourier Transform (1999) is a highly efficient method for computing option prices across a range of strikes using characteristic functions and FFT. It enables rapid pricing of European options under any model with a known characteristic function (Heston, Merton jumps, Variance Gamma), with computati
The Crank-Nicolson method is a widely-used implicit finite difference scheme for solving PDEs in option pricing. It provides second-order accuracy in both space and time, unconditional stability, and can efficiently price derivatives with early exercise features (American options) or complex boundary conditions.
The Longstaff-Schwartz method (2001) is a Monte Carlo algorithm for pricing American options and Bermudan swaptions by approximating the optimal exercise boundary via least-squares regression. It has become the industry standard for pricing path-dependent derivatives where analytical solutions do not exist.
The Price Fairness Scale (PFS), developed by Xia, Monroe, and Cox (2004), measures customer perception of whether a charged price is fair and reasonable relative to value received and market comparison. Price fairness assessment differs from absolute price satisfaction: customers may perceive a price as high but fair i
Value at Risk is a financial risk measure that estimates the maximum loss a position or portfolio could suffer over a fixed holding period at a given confidence level. It is the standard benchmark in risk management and regulatory capital calculations, developed in the textbook tradition of Jorion (2007) and the Basel
Wavelet financial analysis decomposes a financial time series into different frequency bands (time scales) so short- and long-term relationships can be studied at the same time. Drawing on the treatments of Gençay, Selçuk and Whitcher (2001) and Aguiar-Conraria and Soares (2014), wavelet coherence then visualises how t