quantitative_finance

We derive the ATM implied volatility skew power law $\psi(T) \sim C \cdot T^{H-1/2}$ from the rough Bergomi (rBergomi) model through a machine-verified chain of 125 theorems.

We develop a unified error-bound framework for American basket option pricing that decomposes total numerical error into three controllable components: characteristic-function (COS) truncation error, forward-wave (FW) conditioning error, and Gauss-Hermite (GH) quadrature error.

We develop a formal theory of systemic risk cascades and prove that financial contagion exhibits a sharp phase transition at a critical default fraction $D_c = \alpha/\beta$, where $\alpha$ is the absorption rate (capital buffers) and $\beta$ is the contagion rate (bilateral exposure).

We present a formally verified framework for pricing interest rate derivatives using a hybrid approach that combines Nelson-Siegel yield curve dynamics with COS method characteristic function pricing.