# Essentials of QA

Quantitative analysis: A simple overview [ here , Wikipedia ]

Introduction to Quantitative Finance [ text ]

Essentials of Mathematical Concepts for Algorithim Trading [ here ]

Using Digital Signal Processing [ here ] (Zorro codes)

Understanding Quantitative Analysis Of Hedge Funds (standard deviation, skweness, etc) [ here ]

# Topics

FIRST PART

#### 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

#### 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

THIRD PART

#### 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
• Confidence intervals and hypothesis tests for model parameters
• Problems: Heteroscedasticity, autocorrelation and multicollinearity
• Application: The market model

### FOURTH PART

#### MODULE 1: INTRODUCTION TO VBA PROGRAMMING

• The VBA IDE
• Writing a simple function
• Variables, data types and constants
• Subroutines and functions
• Built-in functions and statements
• Program control statements
• Application: A Black-Scholes-Merton option pricer

#### MODULE 2: ARRAYS IN VBA

• Declaring arrays
• Dynamic arrays
• Resizing an array
• Arrays as inputs
• Arrays as outputs
• Application: A Cholesky decomposition function

#### MODULE 3: (SLIGHTLY) MORE ADVANCED VBA TOPICS

• Benefits of explicit variable declaration
• Variable scope: Public, Private and Local
• Error handling
• Debugging code
• The Excel object model

### FIFTH PART

#### MODULE 1: MONTE CARLO METHODS

• Random number generation
• Application: Simulating Brownian motion
• Application: Pricing European options by simulation
• Simulating correlated random numbers
• Application: Simulating correlated default times
• Techniques for accelerating convergence

#### MODULE 2: LATTICE TECHNIQUES

• Fitting a binomial tree to an asset price process
• Application: Pricing an American put on a binomial tree
• Application: Pricing options on dividend paying securities
• Trinomial tree models

#### MODULE 3: FINITE DIFFERENCE TECHNIQUES

• Approximating first and second derivatives by finite differences
• Explicit finite difference technique for derivatives pricing
• Application: Pricing options
• Overview of more robust approaches: Implicit and Crank-Nicolson