rcalxrc08

FinancialToolbox.jl

Black & Scholes in closed form

Pricing, Greeks and implied volatility under the Black and Black & Scholes models, with the same syntax as the Matlab Financial Toolbox.

• Prices and sensitivities: blsprice, blsdelta, blsvega, blsvanna, …
• Implied volatility with the 2024 version of Jäckel's Let's Be Rational: machine precision in at most two Householder steps.
• Date utilities: yearfrac, daysact, Excel date conversion.
• Works with Float32, BigFloat and AD number types.

• Black–Scholes
• Implied vol
• Greeks

FinancialMonteCarlo.jl

Monte Carlo pricing for equity derivatives

Pricing and risk management of equity products by Monte Carlo simulation, from vanillas to early-exercise options.

• Models: Black & Scholes, Heston, Kou, Merton, NIG, Variance Gamma, (shifted) lognormal mixtures; multivariate via Gaussian copula.
• Payoffs: European, barrier, Asian, Bermudan and American (Longstaff–Schwartz).
• Term structures of rates and dividends; pricing straight from an SDE via DifferentialEquations.jl.
• Threads, processes and CUDA; sensitivities through ForwardDiff, ReverseDiff, DualNumbers, TaylorSeries.

• Monte Carlo
• Lévy processes
• GPU

FinancialFFT.jl

Fourier methods for option pricing

Extends FinancialMonteCarlo.jl with Fourier-based pricers that work directly on the characteristic function of the model.

• Methods: Lewis, COS, Carr–Madan, Carr–Madan–Lewis.
• Densities of the log-return via FFT inversion or COS expansion, ready for likelihood-ratio and Vibrato estimators.
• European and binary options, single prices or whole smiles.
• Differentiable with ForwardDiff, ReverseDiff, Zygote, Mooncake and more; runs on CUDA.

• FFT
• COS method
• Characteristic functions

VibratoMonteCarlo.jl

Smooth Monte Carlo Greeks of any order

Plain Monte Carlo estimators are not differentiable, which makes automatic differentiation useless on discontinuous payoffs. This package builds estimators that are C^∞, so sensitivities of any order come out of AD.

• Estimators: likelihood ratio, Vibrato (for any process, not just Itô), Vibrato saltando for finite-activity Lévy.
• Integration: numerical, Monte Carlo (standard, antithetic, Sobol), Gauss–Hermite.
• European, binary and (WIP) American options on Black & Scholes, Kou, Merton, NIG, VG.

• Greeks
• Vibrato
• Automatic differentiation

PatternVectors.jl

Structured vectors, stored as patterns

An immutable AbstractVector that stores a few values and the rule for where they go, instead of every element: think Simpson weights [1, 4, 2, 4, …, 4, 1], alternating signs or boundary values on a grid.

• A tiny isbits object: O(1) memory, ready to be sent to a GPU kernel as is.
• Broadcasts evaluate once per distinct value; mixed with dense arrays they fuse into a single pass, on CPU and GPU.
• O(1) sum and range indexing.
• Differentiable with Zygote, Mooncake and Enzyme, with gradients kept on the pattern values.

• Arrays
• GPU
• Automatic differentiation