Lecture Notes: Introduction to Mathematics in Modern Finance

Course Overview

• History: Course previously held for 6 credits, now expanded to 12 credits with more frequent classes.
• Instructors: Dr. Jake Shaw, Dr. Vasily, Dr. Peter Campston, Dr. Chong Bong Lee.
• Focus Areas:
  • Linear algebra, probability, statistics, stochastic calculus.
  • Application of mathematics in finance.

Course Goals

• To provide a foundation in financial mathematics.
• To help decide career paths in finance.
• Practical exposure through case studies from industry professionals.

Class Structure

• Twice a week sessions.
• Mix of mathematical foundations and real-world financial applications.
• Industry practitioners sharing insights.

Importance of Mathematics in Finance

• Mathematics underpins all financial models and risk assessments.
• Transition in finance industry from intuition-based to quantitative methods.
• Increased need for professionals with strong math and data skills.

Historical Perspective on Markets

• Origins of Markets: Exchange of goods leading to centralized exchanges.
• Types of Markets: Stock exchanges, OTC markets, electronic platforms.
  • Centralized (stock exchanges, futures exchanges) vs. decentralized trading (OTC).

Financial Products

• Types: Equities, loans, bonds, commodities, real estate, derivatives.
  • Equities involve IPO and secondary trading.
  • Loans transform into bonds when securitized.
  • Derivatives include options, swaps, structured products.

Major Market Players

• Banks and Dealers: Role in market-making and risk management.
• Investment Banks vs. Commercial Banks: Differences post-Glass-Steagall.
• Asset Managers, Hedge Funds, Private Equity: Various investment strategies.

Market Dynamics and Trading Strategies

• Types of Trading: Hedging, market-making, proprietary trading.
  • Risk management through hedging and market-making.
  • Strategies include arbitrage, trend following, statistical arbitrage.

Mathematics in Finance

• Applications: Pricing models, risk management, trading strategies.
• Role: Solving differential equations, quantitative risk assessment.

Risk Management Concepts

• Examples: Hedging currency risk, market making, proprietary trading.
• Risk Aversion: Human behavior in financial decision-making.
• Quantitative Measures: Delta, gamma, theta, vega, VAR (Value at Risk).

Homework and Course Resources

• Suggested readings on financial glossary, course website materials.
• Emphasis on understanding financial terminologies and concepts.

Example Projects in Finance

• Delta Estimation Project: Using optimal shift size for derivative estimation.
• Electronic Trading Project: Application of Kalman filter for price prediction.

Class Administration

• Sign-up for class announcements.
• Lectures and additional materials available on the course website.