Mathematics, Probability and Statistics for Finance
This program develops the desk-ready mathematics training essential for quantitative roles in finance, including trading, structuring, valuation, risk management, regulation and financial engineering. Learn all the mathematical techniques that you need to succeed, in an intuitive, accessible fashion.
This course is a component of the Quantitative Methods for Finance Professional Certificate.
Prerequisite knowledge:
- Intermediate MS Excel skills
- Basic calculus
- Basic probablility
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To make it even easier to learn, you can finance your program through Affirm.
Loans offered through Affirm are available in the U.S. and Canada.
Module 1: Mathematical Basics
- Sequences, series and limits
- Application: Annuities, Perpetuities and Coupon Bonds
- Application: Macaulay duration and convexity
- Euler's number
- Application: Continuous compounding
- Exponential and logarithmic functions
Module 2: Derivatives and Differentials
- Tangents, limits and derivatives
- Partial derivatives
- Taylor series expansion of a function
- Application: Modified duration and convexity
- Optimization
- Application: Optimal stopping I
Module 3: Integration
- Definite and indefinite integrals
- Application: Optimal stopping II
- Integration by parts
- Application: Modified duration and convexity for bonds making continuous payments
- Easy differential equations
Module 4: Essential Linear Algebra for Finance
- Systems of linear equations
- Matrix multiplication
- Determinants
- Matrix inversion
- Application: Interpolating yield curves
- Cramer's rule
- Cholesky decomposition
Module 1: Probability
- Probability and random variables
- Distribution and density functions
- Moments of random variables
- Jensen's inequality
- Application: Risk aversion and risk management
- Probability models for finance
- Application: A binomial option pricing formula
- Application: A model for credit risk
- Multivariate probability models
- Covariance, correlation and dependence
- Application: Portfolio mathematics
- Copula functions
- Application: Basket default swaps
Module 2: Stochastic Processes
- Discrete time processes
- Random walks
- Markov and martingale properties
- Application: Pricing options on a binomial lattice
- Continuous time processes
- Brownian motion and Ito processes
- Application: The Black-Scholes-Merton European option pricing formula
Module 1: Essential Statistics for Finance
- Point estimation of population parameters
- Method of moments and maximum likelihood
- Desirable properties of estimators
- Interval estimation
- Application: Value at Risk
- Hypothesis testing
- Type I vs. type II errors
Module 2: Regression Analysis
- Method of least squares
- Linear vs. non-linear models
- Properties of linear model estimators
- Condfidence intervals and hyprothesis tests for model parameters
- Problems: Heteroscedasticity, autocorrelation and multicollinearity
- Application: The market model