MATH-3286: The Mathematics of Finance

• Course Description
  
  
• General Introduction to Financial Mathematics
  
  
  

  LECTURE NOTES

  
  

  STATEMENT:

  Most of lectures in this course are delivered by power point slides, but problem-solving examples will be shown by blackboard writing. Students are required to take lecture notes on problem-solving. Sections labelled with * in lecture notes are reading materials.

  
  

  PART I: FIXED INCOME INVESTMENTS AND RISK-FREE ASSETS

  1. Chapter 1: The Theory of Interest, Annuity, Amortization of Debt and Bond
     Lecture Notes (Normal Format)
     Lecture Notes (Handout Format 1)
     Lecture Notes (Handout Format 2)
  
  
  

  PART II: APPLIED MATHEMATICS AND BASIC FINANCIAL PRINCIPLE PRELIMINARY

  1. Chapter 2: Review on Discrete Probability Theory
     Lecture Notes (Normal Format)
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  2. Chapter 3: Review on Normal Random Variables, Central Limit Theorem and Lognormal Random Variables
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  3. Chapter 4: The Arbitrage Theorem and Linear Programming
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  4. Chapter 5: Discrete Random Walks, Brownian Motion/Wiener Process, Ito's Lemma and Stochastic Calculus
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     Lecture Notes (Handout Format 2)
  
  
  

  PART III: FINANCIAL DERIVATIVES

  1. Chapter 6: Forwards and Futures
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  2. Chapter 7: European Options and the Fundamental Equation Governing the Price of Options: Black-Scholes Partial Differential Equation
     Lecture Notes (Normal Format)
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  3. Chapter 8: Solution of the Black-Scholes Equation and Derivation of the Option Pricing Formula by Binomial Model
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  4. Chapter 12: American Options in Binomial Model Approach
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  PART IV: FINANCIAL ENGINEERING INTRODUCTION

  1. Chapter 9: Greek Parameters
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  2. Chapter 10: Hedging
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  3. Chapter 11: Portfolio Optimization
     Lecture Notes (Normal Format)
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  II. HOMEWORK ASSIGNMENTS

  
  
  1. Homework Assignment 1
     
     
  2. Homework Assignment 2
     
     
  3. Homework Assignment 3
     
     
  4. Homework Assignment 4
     
     
  5. Homework Assignment 5
     
     
  6. Homework Assignment 6
     
     
  7. Homework Assignment 7
     
     
  8. Homework Assignment 8
     
     
  9. Homework Assignment 9
     
     
  10. Homework Assignment 10
      
      
  11. Homework Assignment 11
      
      
  12. Homework Assignment 12