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.
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
Desk-Ready Skills
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
Portfolio managers, risk managers, traders, desk quants, research analysts, regulators, aspiring financial engineers and anyone seeking to develop the skills necessary to understand quantitative finance.
Prerequisite knowledge:
Intermediate MS Excel skills
Basic calculus
Basic probablility
Jack Farmer
Jack is currently the Curriculum Director for the New York Institute of Finance. Farmer also acts as an outside adviser for portfolio managers at significant global investment funds. These funds included emerging markets equity funds and global macro hedge funds. Jack serves a variety of functions for the funds he advises, including the development of options strategies, quantitative strategies, and hedging strategies. Additionally, Jack specializes in capitalizing on systemic and macroeconomic imbalances in equity and fixed income markets throughout the world.
Jack specializes in training and consulting solutions for portfolio risk management, FX and interest rate derivatives and trading, equity index and volatility trading, equity derivatives and structured equity products, financial statement analysis and hedge accounting.
Education
BS in Engineering from Tulane University MBA in Finance and Accounting from Tulane University Ph.D. in Finance (ABD) from the University of Texas at Austin
Khosrow Mehrzad
Khosrow has broad experience in capital market, financial products, micro and macro analysis, and portfolio management. Khosrow founded Parsa Capital Management in 2015, where he manages an equity fund. Khosrow joined JP Morgan as analyst responsible for hedging, risk management and structuring for two special situation investment funds with over $1 billion in assets. He later became a senior portfolio manager responsible for relative values trades and spearheaded firm’s effort in launching hedge funds. Khosrow was a senior valuation analyst at Six Financial Information, responsible for pricing exotic derivatives. He also managed a team of analysts, and led the process of migrating the models from PC environment to company’s main computing platform. Khosrow worked as Co-CIO at AlphaEngine Global Investment Solutions, a startup hedge fund where he developed the tactical asset allocation models. Khosrow was a Director at Deutsche Bank Advisors oversaw a team of analysts located in India, conducted fundamental analysis of US equities, and managed an equity proprietary book. Khosrow received a BS from Sharif University of Technology, a MS from McGill University, and earned an MBA from MIT Sloan School of Management.
