Computational Finance

A collection of computational-finance scripts: MATLAB scripts for portfolio optimization, yield-curve bootstrapping, and optimal trade execution, plus R scripts for Monte Carlo simulation and sampling methods.

MATLAB scripts

Script	Description
Markowitz.m	Mean-variance portfolio optimization on a 10-stock universe: plots the efficient frontier, the global minimum-variance portfolio, the tangency portfolio (capital market line), and constrained frontiers (no short selling; sector-weight bounds) solved via quadprog.
yieldCurve.m	Bootstraps a zero-coupon yield curve from five semi-annual coupon bonds (maturities 1, 2, 3, 5, 10 years), then computes yield-to-maturity, Macaulay duration, and duration for each bond, and plots the curve.
f.m	Helper for yieldCurve.m: prices a coupon bond with previously bootstrapped yields, leaving the last segment's yield as the unknown (root-found with fzero).
g.m	Helper for yieldCurve.m: bond price minus market price as a function of a single flat yield, used to solve for yield-to-maturity.
almgren_chriss.m	Monte Carlo simulation of optimal liquidation under the Almgren-Chriss model, comparing terminal-wealth mean/std frontiers for constant vs. stochastic (mean-reverting) temporary price impact across risk-aversion levels.
getMarketData.m	Downloads historical market data from Yahoo Finance (fork of Artem Lenskiy's downloader). Used by Markowitz.m to fetch prices. Note: the Yahoo endpoint it targets has changed over the years and may require updating.

Running

Open MATLAB in the repository root and run any script, e.g.:

yieldCurve
almgren_chriss
Markowitz   % needs price data; see get_prices() inside the script

Requirements: yieldCurve.m uses the Symbolic Math Toolbox (syms, symsum); Markowitz.m uses the Optimization Toolbox (optimvar, quadprog). Scripts relying on those toolboxes will not run in stock GNU Octave; the others (almgren_chriss.m) are Octave-compatible.

Monte Carlo (R scripts)

Script	Description
Monte Carlo/european_call.R	Prices a European call under Black-Scholes dynamics by Monte Carlo with antithetic variates; reports the price estimate with a 95% confidence interval.
Monte Carlo/areas.R	Monte Carlo integration of 1, x, x², sin(x), exp(x) on [0, 1], showing estimator convergence as the sample count grows.
Monte Carlo/multivariate_area.R	Monte Carlo integration of exp((x + y)²) over the unit square.
Monte Carlo/order_statistics.R	Samples order statistics (min/max of uniforms, min of exponentials) via inverse-CDF formulas and validates against empirical simulation.
Monte Carlo/poisson_sampling.R	Generates Poisson samples from exponential inter-arrival times and compares mean/variance against R's rpois.
Monte Carlo/rejection_sampling.R	Rejection sampling from f(x) = 2(1 − x) on [0, 1] using a uniform proposal.
Monte Carlo/stickToTriangle.R	Estimates the probability that a stick broken at two uniform points forms a triangle (analytic answer: 1/4).

Running

Rscript "Monte Carlo/european_call.R"

No external R packages required (base R only).