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Introduction

Shoals is a quantitative-finance library for the Chelis programming language. It is available as a Reef package under the Shoals module prefix. It provides closed-form option pricers, Greeks, Monte Carlo engines, yield-curve and volatility-surface tooling, risk measures, date and calendar arithmetic, an order book, and a small set of finance-specific distributions.

The library is written entirely in Chelis. Numerical primitives that are not finance-specific (the normal distribution, special functions, statistics, interpolation) come from Nautilus, and the date type comes from Std.Datetime.

Modules

Section titled “Modules”
  • Pricing. Black-Scholes call and put, vectorized price tensors, and a Monte Carlo engine driven by explicit random keys.
  • Greeks. Finite-difference first- and second-order Greeks, analytic Greek references for cross-checking, and pathwise / likelihood-ratio estimators for the digital payoff family.
  • Extended pricers. Bachelier (normal underlying), Black (forward), Garman-Kohlhagen (FX), Margrabe and Stulz (exchange), and digital options.
  • Volatility surface. SVI total-variance parameterization, implied vol, surface shifts, a SABR approximation, and a bisection implied-vol solver.
  • Stochastic processes. Geometric Brownian motion paths and terminals, antithetic variates, Merton and Kou jump-diffusion, Heston quadratic-exponential simulation, and correlated two-asset GBM.
  • Risk. Parametric and historical value-at-risk and conditional VaR.
  • Extended risk. Monte Carlo VaR and expected shortfall, an FRTB-IMA expected-shortfall helper, a scenario PnL grid, and the Kupiec proportion-of-failures, Christoffersen, and Acerbi-Szekely backtests.
  • Yield curves. Linear, spline, log-linear, and Nelson-Siegel-Svensson interpolation, discount factors, a single-curve par bootstrap, a deposit/zero-coupon/par-swap instrument bootstrap with IFT sensitivities, curve-kind metadata, and sensitivity operators.
  • Dates, tenors, schedules. Exact-rational day-count conventions, calendar-month tenors, business-day money-market tenors and spot lags, and anchored coupon schedules, over Std.Datetime and Shoreleave market calendars.
  • Market data. Quote, bar, and snapshot record types.
  • Order book. A price-priority limit order book with best bid and ask, spread, and volume-weighted average price.
  • Distributions. Lognormal, Student-t, and bivariate-normal densities, gamma, beta, chi-squared, exponential, uniform, and Poisson wrappers, and a multivariate-normal sampler.
  • Calibration. Weighted residuals, sum-of-squared-errors loss, and bounded Levenberg-Marquardt and BFGS fits.
  • XVA. Exposure aggregation, netting, CVA and DVA, plus funding and capital adjustment helpers.
  • Currency-tagged money. Runtime-tagged Money with same-currency arithmetic.
  • Lattices, PDEs, and early exercise. CRR, Tian, Jarrow-Rudd, and trinomial trees (Shoals.Trees), Crank-Nicolson and ADI finite differences (Shoals.Pde), Longstaff-Schwartz (Shoals.Lsm), and fixed-coupon bond prices (Shoals.FixedIncome).
  • Rate and volatility models. One- and two-factor Hull-White short-rate models (Shoals.HullWhite), the LIBOR market model and HJM drift (Shoals.LiborMarketModel), SABR paths (Shoals.SabrPaths), Heston Fourier pricers (Shoals.Heston), and Dupire local volatility (Shoals.Dupire).
  • Credit default swaps. Hazard curves, CDS legs, and a par-spread bootstrap (Shoals.Cds).
  • Quasi-random points. Sobol and Halton sequences and variance-reduction estimators (Shoals.Rng), in the stochastic-processes chapter.
  • Collateral. CSA threshold, minimum transfer, and haircut (Shoals.Csa), in the XVA chapter.

Each module chapter gives its public functions with their signatures, input domains, and failure behavior.

Comparisons and supported domains

Section titled “Comparisons and supported domains”

The Textbook references and Property specifications chapters describe comparisons with standard formulas and finance relationships. The Scope and limitations chapter summarizes the supported models and numerical domains.

Start with a pricing call

Section titled “Start with a pricing call”

Start with Getting started for the build commands and a first pricing call, then read Working with tensors and keys for tensor ownership and reproducible random calls. Each module chapter includes its public functions and examples.