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

SECOND PART


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
 
 
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
  • Reading files
  • 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

 

 

 

 

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