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Topics in Mathematics with Applications in Finance (MIT 18.642)

by Peter Kempthorne, Vasily Strela, Jake Xia · MIT OpenCourseWare

Pairs mathematics lectures on linear algebra, probability, statistics, stochastic processes and numerical methods with practitioners' lectures on applications: time series, volatility modeling, portfolio theory and option pricing. Includes 22 lecture videos, slides, readings and problem sets for building working fluency in quant-finance mathematics.

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numpy-financial – Financial Functions for Python

Official documentation for numpy-financial, the NumPy project's package of elementary financial functions split out of NumPy itself. It covers net present value, internal rate of return, payments, interest rates and future value, so you can compute loan and investment cash-flow figures in Python.

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QuantLib – Open-Source Quantitative Finance Library

Home of QuantLib, the free open-source C++ library for quantitative finance with Python bindings. It implements yield-curve bootstrapping, interest-rate and equity derivative pricing, Monte Carlo and finite-difference engines, and market calendars, letting practitioners build and test production-grade pricing and risk models.

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AbsBox – Open-Source ABS/MBS Cashflow Modeling Library

Open-source Python library, released under Apache 2.0, that wraps the Hastructure cashflow engine for structured finance. It models pools of mortgages, auto loans, leases and corporate loans, defines deal waterfalls in readable code, and runs pool-performance sensitivities to forecast and price ABS and MBS tranches.

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Introduction to Financial Engineering and Risk Management

Columbia University's introductory course in financial engineering, reviewing probability and optimization, then pricing fixed income securities and swaps, and valuing options with one-period and multi-period binomial models and Black-Scholes. Learners can price standard derivatives in an arbitrage-free framework.

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Quantitative Finance Stack Exchange

Moderated Q&A site where practitioners and academics answer questions on pricing models, calibration, volatility surfaces, risk measurement and market microstructure. Use it to resolve specific modelling and implementation problems and to see how professionals justify their reasoning. Voting and moderation give it a verification mechanism no blog or Discord has.

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Advances in Financial Machine Learning

Lopez de Prado's treatment of machine learning on financial data: alternative bar sampling, triple-barrier labelling, fractional differentiation, purged cross-validation and backtest overfitting. It shows why naive ML backtests fail and how to structure ones that survive. Covers the modern buy-side quant workflow that the classical pricing texts do not touch, and its core contribution is methodological rather than tactical: it teaches why standard cross-validation and Sharpe-ratio reporting produce false discoveries on financial data. That mental model transfers to any research process.

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