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

• 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), and Margrabe (exchange).
• 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 jump-diffusion, 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 backtest statistic.
• 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.
• Calibration. Weighted residuals, sum-of-squared-errors loss, and a bound-clamped Levenberg-Marquardt step.
• XVA. Exposure aggregation, netting, CVA and DVA, plus funding and capital adjustment helpers.
• Currency-tagged money. Runtime-tagged Money with same-currency arithmetic.

Additional modules cover lattice and PDE pricing, fixed-income models, collateral agreements, credit curves, local volatility, Longstaff-Schwartz exercise, and specialized stochastic processes. The module guides describe their public functions and numerical domains.

Comparisons and supported domains

The Reference oracles 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

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.