Quantitative Finance Syllabus Overview

Course Introduction

• Instructor: Ensign Gupta, Bartman IIT Kanpur
• Course Focus: Quantitative Finance

Course Components

1. Tools and Techniques
   • Mathematical Techniques
   • Statistical Techniques
   • Simulation Techniques
   • Computational Techniques
2. Application in Finance
   • Portfolio Analysis
   • Derivative Pricing
   • Stock Price Analysis
   • Risk Analysis

Detailed Syllabus

Key Areas of Study

1. Quantitative Techniques in Finance
   • Mathematical, statistical, simulation, and computational tools used in finance
   • Applications to portfolio analysis, derivative pricing, stock price analysis, risk assessment
2. Interest Rates and Present Values
   • Net present values (NPV), continuous compounding
   • Internal rate of returns (IRR)
   • Application to portfolio and investment strategy balancing
3. Time-Series and Econometric Techniques
   • Linear regression, multiple linear regression
   • Capital asset pricing model (CAPM)
   • Market line, beta analysis
4. Factor Models in Finance
   • Single and multi-factor models
   • Arbitrage Pricing Theory (APT)
5. Risk Management
   • Risk aversion, pricing, probability distributions (normal/non-normal, extreme value)
6. Derivatives and Derived Products
   • Forwards, futures, options, exotic options, swaps
   • Risk minimization strategies using derivatives
   • Multi-period securities, Value at Risk (VaR), Conditional Value at Risk (CVaR)
   • Copula theory, market risk, operational risk

Tools and Techniques

1. Economic Theory Applications
   • Microeconomic principles: Supply & Demand, price optimization
   • Estimation and utility theory applications
2. Probability and Statistics
   • Law of large numbers, Bayesian theorem, conditional probabilities
   • Various probability distributions: Normal, Gumbel, Pareto
3. Mathematical Methods
   • Multivariate functions, numerical techniques (e.g., Newton-Raphson)
   • Stochastic processes, random walks, martingales, ergodic theory
4. Optimization Methods
   • Markowitz Portfolio Optimization
   • Dynamic programming, stochastic programming, robust optimization
5. Time-Series Methods
   • ARIMA, GARCH models
   • Applications in CAPM and APT models with practical examples
6. Computational Techniques
   • Monte Carlo simulations, MCMC methods
   • Usage in portfolio analysis and option pricing

Reference Materials

• Books:
  • "Investment Analysis and Portfolio Management" by Prasanna Chandra
  • "Introduction to Operations Research" by David G. Luenberger
  • "Options, Futures, and Other Derivatives" by John C. Hull
  • "Modern Portfolio Theory and Investment Analysis" by Edwin J. Elton
  • "An Introduction to Quantitative Finance" by Stephen Blyth
  • "Statistics and Finance: An Introduction" by David Ruppert

Important Points

1. Not an Investment Course
   • This course does not focus on stock market investment strategies.
   • No in-depth study of fundamental or technical analysis.
2. Target Audience
   • Students interested in quantitative finance.
   • Aim to address the lack of good faculty and resources in this field.

Course Delivery

• Methodology: PPT-based lectures, occasional use of board, computer, and online resources.
• Practical examples and case studies.

Next Steps

• Start with an introduction to basic concepts in economics and utility theory related to demand and supply.
• Subsequent lectures will build on these foundations to delve into quantitative finance topics.