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derivatives-pricing

derivatives pricing engine

Monte Carlo, PDE pricers

SystemTechniques · 4Primitives · 21 derivatives-pricing Binomial lattice pricingfinance · medium: Recombining price tree with risk-neutral probabilities and backward induction; the cheapest way to price early-exercise claims, O(N²) time and O(N) memory.›Least squares monte carlofinance · medium: Longstaff-Schwartz regression for early-exercise options in Monte CarloYield curve bootstrappingfinance · medium: Turn quoted deposits, futures and swaps into a discount curve by solving one new maturity per instrument so that every quote reprices exactly.›Levenberg marquardtnumerics · medium: Damped Gauss-Newton nonlinear least squares for model calibrationBlack-Scholes-Merton formulafinance · low: Closed-form European option price and Greeks from spot, strike, time, rates and volatility; Newton inversion gives implied volatility. About 30 ns each.›Day count conventionsfinance · low: ACT/360, ACT/365, 30/360, ACT/ACT accrual fractions for interest and couponsLow discrepancy sequencesnumerics · low: Sobol, Halton and blue-noise sequences with scrambling for quasi-Monte CarloMonte Carlo integrationnumerics · low: Estimate an expectation by averaging random samples; error falls as σ/√N in any dimension, and variance reduction (antithetic, control variates, importance sampling) shrinks σ.›Newton root findingnumerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.›Spline interpolationnumerics · low: Linear, bilinear/trilinear and cubic spline interpolation on grids and tablesFinite differencesnumerics · low: Replace derivatives with weighted differences of grid values; simple stencils plus a stability condition (CFL) turn PDEs like heat, advection and waves into array loops.›LU and Cholesky factorizationnumerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).›SIMD programminghardware-os · low: Process 4-16 lanes per instruction with AVX2, AVX-512 or NEON via Rust std::arch, with runtime dispatch and a portable fallback.›CUDA and GPU languageslanguages · low: Programming GPUs: thousands of lockstep threads, bound by memory bandwidth; libraries first, Triton for fused kernels, CUDA C++ for peak speed.›Reverse-mode automatic differentiat…ml-training · low: Record the forward computation on a tape, then sweep it backwards once to get the gradient of a scalar loss for all inputs.›Fast Fourier transformnumerics · low: Computes the DFT in O(n log n) by recursively splitting into even and odd halves; the basis of fast convolution and spectral methods.›Floating-point errornumerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.›L-BFGSnumerics · low: Quasi-Newton minimizer that approximates the inverse Hessian from the last m gradient differences via the two-loop recursion; O(m·n) memory and work per step.›PRNGs (PCG, xoshiro)numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.›Thomas tridiagonal solvernumerics · low: O(n) tridiagonal linear solve used in implicit finite-difference and spline schemes+ 5 more primitives

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