Introduction to Quantitative Finance with Python

Linear and Quadratic Functions, Continuous and Differentiable Functions, Definition of Differentiation using Limits, Discontinuous Functions and its applications to quant finance, Exponential function and Taylor series, Natural Logarithm,  Monotonic Concave and convex functions, Stationary points and how it relates to optimization.

Topics in Multivariable Calculus, Partial Derivatives, Hessian Matrix, Unconstrained Optimization-Lagrange, and Multi-variate Taylor Series Expansion.

Matrix Algebra, Singular Matrix, Identity Matrix, Inverse of a Matrix, Definite Matrices, Singular Matrix, Eigenvalues and eigenvectors, Characteristic Equation, Matrix Decompositions

Using Fundamental Ideas from linear algebra to understand the Linear Regression Model.

We cover laws of probability, idea of pdf and cdf, expected value and variance, covariance and correlation, skewness and kurtosis.  (Note: The jupyter notebook for this lecture, will be the same notebook used throughout this section except for numerical methods. )

Talk about Discrete statistical distributions, ie) Binomial, Poisson and More.  Give some finance examples, especially how Poisson can be applied. 

Discuss continuous statistical distributions ie) Normal, Log Normal, Exponential, Normal Mixture and More.

Cover the idea behind the bivariate pdf, multivariate pdf, and multivariate normal distribution. We also cover statistical inference.

We cover the maximum likelihood estimation.  We solve the maximum likelihood estimates for the normal distribution and the binomial distribution.

We cover the theoretical aspects of linear regression and give an example using OLS from the stats models package. I discuss how OLS is used in quantitative finance.

Newton Rhapson, Gradient Descent, BFGS and L-BFGS Optimization techniques are discussed.

Discuss Black Scholes Option Formula , solve for parameters using Newton Rhapson, discuss Greeks.

We discuss the Capital Asset Pricing Model

We discuss the basics of portfolio theory. Efficient frontier and more are discussed.  We use MSFT and GLD as examples.

I discuss central banks, macroeconomics, the risk free rate and yield curve, and asset pricing. ( Note: In order to run certain parts of the notebook, the yield curve inversion for the 2008 financial crisis, you are going to need to have your own FRED(Federal Reserve) API key.  I give the link as an external resource.

I discuss the balance sheet, income statement, and statement of cash flows.

I discuss the capital structure and some financial ratios that are derived from financial statements.

We use the opensource package financetool kit to look at financial ratios more in depth.  At the end, we merge this to price data, so that we can eventually run regression models on them. (Note: you must have an API Key for this, please refer to the external link and sign up for one. They have multiple pricing options, but you can sign up for the FREE version).

We use fundamental factors (ie Financial Ratios) and use Regession Analysis to gain insights.  This time Yahoo Finance is used for Financial Ratios.

We talk about the basics of bond analysis. Duration, YTM are discussed. Yield Curve is discussed as well.

I discuss financial metrics such as the Sharpe Ratio, Volatility, Draw Down and More. This section is useful when we look at modeling especially for machine learning. 

Here we learn how to conduct basic plotting,  calculate returns, and log returns. By the end we compare a technical analysis trading strategy with a simple buy and hold.

We discuss the ideas of the ARIMA model ie) Stationary Series, AIC, etc.

We discuss the ideas of GARCH model, how it differs from ARIMA, and how volatility is modeled. 

We implement ACF and PACF,  and Augmented Dickey Fuller Test a stationarity test. We use a hybrid model ARIMA GARCH to build a trading strategy. 

Monte Carlo Simulation, Multi Asset Correlation, and Stochastic Volatility.

This is a tutorial discussing GRADIO, a web application.  We discuss the basic ideas so that we can later build a web application for trading.

We discuss the idea of Cointegration and Pairs Trading.  Cointegration, in essence, builds a synthetic asset. ( a combination of the return and risk profiles of two stocks). Synthetic Assets are constructed using statistical based ideas such as stationarity and OLS. A pair trading example is shown, using Pepsi and Coke.

We use GRADIO to build a pairs trading web application.  Students are encouraged to pick two stocks and see if they are cointegrated. 

I discuss rules based trading, machine learning based trading and discuss some ideas about feature engineering. The open source package pybroker is used.  Students are encouraged to experiment with financial ratios and input them into machine learning models to see what type of trading results they get.

I discuss event analysis, where one date is picked out and window is built around it. We examine if an event is statistically significant based on the stock returns generated in this window.   In this video, I show that Trumps Tariffs caused an effect on Apple, who does business with China, but Microsoft was less affected.  Students are encouraged to pick events they think would be significant, and see how that would affect the equity returns of their choice.

We take the hugging face transformers FINBERT package and conduct Sentiment Analysis on part of an earnings call transcript for a stock.   Students are encouraged to find earnings call transcripts via YAHOO Finance, Federal Reserve Announcements, and News Articles, to detect sentiment and make investment decisions based on this analysis.