MQF

Mathematics for quantitative finance.

• For educational purposes only
• Work in progress
• ~7200 lines of code

Features

Data Acquisition

• Parsing historical data from Yahoo Finance

Chrono

• Gregorian calendar
• Day count conventions
• Time of day in nanoseconds
• Formatted time of day (hh:mm:ss.ms'us'ns)

Probability and Stochastic Processes

Probability Distributions

• Bernoulli
• Beta
• Binomial
• Bivariate Normal
• Cauchy
• Chi
• Chi-squared
• Continuous Uniform
• Dirac Delta
• Discrete Uniform
• Exponential
• F
• Folded Normal
• Gamma
• Geometric
• Gumbel
• Half-Logistic
• Half-Normal
• Inverse Chi-squared
• Inverse Gamma
• Laplace
• Levy
• Log-Cauchy
• Log-Logistic
• Log-Normal
• Logistic
• Maxwell--Boltzmann
• Multinomial
• Negative Binomial
• Normal
• Poisson
• Rayleigh
• Student's T
• Student's T with Location-Scale
• Triangular
• Wald
• Weibull

Copulas

• Ali--Mikhail--Haq
• Clayton
• Comonotonicity
• Countermonotonicity
• Farlie--Gumbel--Morgenstern
• Frank
• Galambos
• Gumbel
• Husler--Reiss
• Independent
• Joe
• Marshall--Olkin
• Plackett

Stochastic Processes

• Wiener / Brownian Motion
• Brownian Bridge
• Geometric Brownian Motion
• Ornstein--Uhlenbeck / Vasicek
• Square-Root / CIR
• Exponential Vasicek
• Binomial Tree
• Trinomial Tree
• Gamma
• Poisson

Numerical Methods for SDEs

• Euler--Maruyama
• Milstein
• Stochastic RK1

Statistics

Descriptive Statistics

• Sample Mean
• Sample Variance
• Sample Covariance
• Sample Correlation
• Sample Skewness
• Sample Excess Kurtosis
• Min
• Max
• Range
• Geometric Mean
• Harmonic Mean
• Histogram Generation
• Empirical Distribution
• Kernel Density Estimation

Kernels

• Cosine
• Epanechnikov
• Gaussian
• Logistic
• Quartic
• Silverman
• Triangular
• Tricube
• Triweight
• Uniform

Regression

• Ordinary Least Squares
• Generalized Least Squares
• Polynomial Regression
• Kernel Regression

Maximum Likelihood Estimation (MLE)

• Bernoulli
• Exponential
• Geometric
• Maxwell--Boltzmann
• Normal
• Poisson
• Rayleigh
• Wald

Method of Moments Estimation

• Chi
• Chi-squared
• Exponential
• Gamma
• Geometric
• Gumbel
• Laplace
• Logistic
• Maxwell--Boltzmann
• Normal
• Poisson
• Rayleigh
• Student's T
• Student's T with Location-Scale
• Wald

Nonlinear Optimization

• Brute Force Grid
• Differential Evolution
• Sequential Minimal Optimization

For Smooth Cost Functions on Riemannian Manifolds

• Line Search
• Gradient Descent
• Conjugate Gradient
• Fletcher--Reeves
• Polak--Ribiere
• Hestenes--Stiefel
• Conjugate Descent
• Dai--Yuan

Time Series Analysis

• Exponential Moving Average
• Double Exponential Moving Average
• Simple Moving Average
• Weighted Moving Average
• Autoregression
• Shift Operator
• Finite Difference Operators

Portfolios

• Efficient Frontier
• Unconstrained
• Fully-Invested
• Capital Asset Pricing Model (CAPM)
• Black--Litterman

Trading

• Portfolios
• Backtest
• Stochastic Test

Test Results

• Return
• Log Return
• Volatility
• Sharpe Ratio
• Drawdown
• Max Drawdown

Indicators

• Moving Average Convergence/Divergence (MACD)
• Relative Strength (RS)
• Relative Strength Index (RSI)

Utility Functions

• Exponential
• Logarithmic
• IsoElastic
• Absolute Risk Aversion
• Relative Risk Aversion

Finance

Interest Rates

• Accumulation factor
• Discount factor
• Conversion between continuous and non-continuous conversion periods.

Pricing

• Black--Scholes pricing for European options
• Zero Coupon Bond
• Fixed Coupon Bond
• Floating Rate Note
• Flat Yield Curve
• Nelson--Siegel Curve
• Svensson Curve

Other

• Fibonacci Numbers
• Fibonacci Ratios

Polynomials

• Chebyshev
• Hermite
• Legendre

Functions

• Factorial
• Binomial Coefficient
• Beta
• Digamma
• Trigamma

Numerical Methods for PDEs

• Rectangular grid in n-dimensions
• Finite differences for partial derivatives, laplacian
• Multi-Index

Dependencies

• Eigen for linear algebra