Numerical Methods for Quants
What you get
A comprehensive, desk-oriented field manual for quantitative researchers, developers, and risk professionals. Spanning 93 pages with custom TikZ vector diagrams, practitioner insights, novel quant tricks, and 50 curated interview Q&As, this book is designed specifically to help you master options pricing, calibration, finite differences, finite elements, and machine learning in computational finance.
Included in the download
93-page PDF: Numerical Methods for Quants: The Master Field Manual
Complete mathematical derivations and proofs (Newton-Raphson quadratic convergence, Crank-Nicolson stability, Dupire's local volatility, and weak formulations)
Detailed, runnable Python/PyTorch implementations for SABR calibration, Leisen-Reimer trees with Peizer-Pratt inversion, COS method option pricing, Crank-Nicolson barrier option pricing, Deep BSDE solvers, and Physics-Informed Neural Networks (PINNs)
Boxed "Equation Shortcuts" under complex formulas for rapid desk problem solving
Custom visual TikZ diagrams in every single module for intuitive comprehension
A dedicated "Novel Quant Trick" section in each module outlining production hacks used on real option desks
A dedicated "Proportional Scaling Relationship" box in each module to quickly grasp how errors and grids scale
50 high-yield, interview-style questions with detailed, context-rich answers
What's covered (high-level)
1. Root Finding & Optimization: Bisection, Newton-Raphson, Secant, Nelder-Mead simplex, and SABR volatility calibration
2. Yield Curve Interpolation & Surface Construction: Linear, log-linear, cubic splines, B-splines, Hagan-West Monotone Convex yield curves, and Gatheral's SVI volatility parameterizations
3. Finite Difference Methods: Theta schemes, Crank-Nicolson, boundary conditions, Rannacher smoothing, and ADI splitting (Douglas-Rachford, Craig-Sneyd) for Heston
4. Monte Carlo Methods: SDE discretization (Euler-Maruyama, Milstein), Heston QE scheme, variance reduction (Antithetic, Control Variates), Sobol sequences, and Brownian Bridge barrier correction
5. Tree & Lattice Methods: CRR binomial trees, Leisen-Reimer trees with Peizer-Pratt inversion, trinomial trees, and transition probabilities
6. Fourier & Spectral Methods: Characteristic functions, Carr-Madan FFT pricing, the COS method, and kurtosis-adaptive domain truncation
7. Volatility Surface Construction: Dupire's local volatility derivation, SVI calibration, and local vol vs stochastic vol smile dynamics (Sticky Strike vs Sticky Delta)
8. Convergence, Stability & Performance: Von Neumann stability analysis, CFL conditions, double-precision precision limits, and Numba JIT compilation
9. Finite Element Methods: Weak formulations, Galerkin method, Delaunay triangulation, local stiffness and mass matrices, and mass lumping
10. Machine Learning in Numerical Finance: PINNs with hard boundary constraint ansatzes, and Deep BSDE solvers for high-dimensional options
Who this is for
Aspiring quants, risk managers, pricing developers, and computational finance graduates preparing for buy-side/sell-side interviews or working on pricing platforms.
Disclaimer
This manual is for educational and informational purposes only. It does not constitute investment, legal, tax, or financial advice. No guarantees are made regarding interview outcomes or performance improvements.
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