Lectures

• 

  1. The Mathematical Finance Toolkit

  In our introductory lecture, Dr. Wilmott presents the foundations of mathematical finance, covering key tools such as exponential and logarithmic functions, Taylor series, and core probability concepts including distributions, expectations, variance, and standard deviation. He also covers the central limit theorem and how random processes lead to normal distributions, commonly used in modeling financial markets. These ideas form the mathematical backbone for applications like derivatives pricing, portfolio theory, and risk management.
• 

  2. Core Concepts in Investment

  In lecture two, we learn about the core principles of fixed income and interest rates, including floating vs. fixed rates, simple vs. compound interest, and the importance of basis points in financial calculations. We utilize concepts from the first lecture, such as exponentials and logarithms, and apply them to bond pricing, yields, and forward rates. Through practical examples, Dr. Wilmott demonstrates how to value future cash flows and extract interest rates from market prices, and concludes with a critical look at credit risk modeling, highlighting the tension between mathematical elegance and real-world accuracy in quantitative finance.
• 

  3. Stock Market Behavior

  In lecture three, we explore quantitative finance applied to stocks, focusing on why simple mathematical models succeed despite their assumptions. Using nearly 100 years of S&P 500 data, Dr. Wilmott shows that markets experience extreme events more often than standard theories predict, yet practitioners still favor the tractable lognormal random walk model. The lecture concludes by deriving the key mathematical model where stock prices follow a geometric Brownian motion, noting that while this model captures about 70% of equity behavior accurately, it has important limitations, especially around extreme events.
• 

  4. Financial Modeling

  In lecture four, Dr. Wilmott introduces simulations, like the Monte Carlo simulation, as powerful tools for modeling stock prices. Through hands-on Excel examples, he shows how randomness, growth, and volatility combine to generate many possible future price paths. By running repeated simulations, we uncover the range of outcomes and the characteristic distribution of stock prices. The lecture highlights a key insight: volatility can be estimated with some confidence, while growth rates are far more uncertain. Finally, we conclude by exploring practical uses like scenario analysis and the challenges of relying on limited historical data.
• 

  5. Portfolio Theory & Investment Strategies

  In lecture five, we investigate portfolio theory and mathematical strategies for investing, beginning with the Kelly criterion—a formula from gambling that determines optimal bet sizing to maximize long-term growth rate. We examine how this concept applies to finance through portfolio construction, introducing key concepts like the Sharpe ratio and correlation between assets. The lecture culminates in Harry Markowitz's Nobel Prize-winning Modern Portfolio Theory, which demonstrates how diversification creates an efficient frontier of optimal portfolios that maximize expected return for given risk levels, though we note practical limitations due to unstable parameters like correlations, especially during market crashes.
• 

  6. Options Trading

  In lecture six, we delve into options trading and valuation, exploring how options give the holder the right to buy or sell an asset at a predetermined price, and the mathematical framework used to determine their fair value. We examine the Black-Scholes-Merton approach alongside the binomial model, which uses hedged portfolios to eliminate risk and avoid subjective probabilities. The lecture concludes with risk-neutral pricing, showing how institutions profit through hedging while speculators face genuine risk exposure.
• 

  7. Investor Behavior

  In lecture seven, we study behavioral finance, showing how traditional theories based on rational decision-making often fail to explain real market behavior. We examine concepts like the efficient market hypothesis and utility theory alongside real-world actions such as lottery play, poor diversification, and cognitive biases like anchoring and herding. The lecture concludes by applying mathematical models to behavioral phenomena, showing how factors like loss aversion and observation frequency impact investor happiness and portfolio selection, arguing that while people are irrational, these patterns can be understood—and even exploited—in finance.
• 

  8. AI in Finance

  In our eighth and final lecture, we explore the differences between machine learning and classical mathematical modeling, examining three main categories: supervised learning, unsupervised learning, and reinforcement learning. We discuss various techniques including k-nearest neighbors, neural networks, and self-organizing maps, illustrated through examples ranging from computers playing tic-tac-toe, to financial applications analyzing volatility regimes, and CEO speeches. Dr. Wilmott concludes that while machine learning always produces results by extracting insights from vast amounts of data, these outputs may not always align with intended objectives, highlighting the importance of careful testing and interpretation.