# Mathematics, Probability and Statistics for Finance

• 3 days
• in person

## What are the topics?

New York Institute of Finance

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## Who should attend

• Portfolio managers
• risk managers
• desk quants
• research analysts
• regulators
• aspiring financial engineers and anyone seeking to develop the skills necessary to understand quantitative 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

*CURRICULUM *

Day 1

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

Day 2

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

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

Day 3

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

WHAT YOU'LL LEARN

• Understand the mathematical stucture of bond pricing
• Understand the application of Taylor series for computing risk measures for bonds and derivatives
• Learn how to apply the tools of linear algebra for portfolio modeling
• Develop a deep appreciation for Jensen's inequality and its ubiquity in financial models
• Develop insights into the structure of stochastic processes and the implications for derivatives pricing
• Learn the essential techniques of statistical inference for finance
• Learn regression analysis in Excel

Mathematics, Probability and Statistics for Finance at New York Institute of Finance

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