Academic Programs > Master Programs > Mathematics for Finance > Session Schedule
The Summer School in Mathematics for Finance is divided into five modules:
Functions of one and several real variables. Functions in Excel and VBA.
Limits of sequences and functions. Convergence. Studying limits in Excel.
Derivatives in one and several variables. The Chain Rule. Taylor series.
Ordinary and partial differential equations. Basic numerical methods in Excel and VBA.
The Riemann integral. Integration techniques. Numerical Integration in Excel and VBA.
Financial applications: Interest rate risk. Bond duration and convexity.
Financial applications: options contract and option-pricing functions.
Financial applications: The Black-Scholes PDE and Black-Scholes formulae.
Financial applications: The Greeks. Delta and Gamma hedging. Exotic options
Discrete and continuous random variables. Distribution functions.
Expectation and variance, higher moments. Moment generating function.
Conditional probability. Conditional expectation. Independence.
Law of large numbers. Central limit theorem. Random walk.
Financial applications: Gambling and fair games. Arbitrage. States of the world.
Financial applications: The binomial method. Risk-neutral probabilities.
Financial applications: Important probability distributions in finance. Fat tails.
Financial applications: Stochastic processes. Brownian motion. Volatility.
Bond pricing and yields. Duration and convexity. Forward rates.
Measures of risk and return. Short sales. Leverage. Volatility and Correlation.
The Efficient Market Hypothesis. The Random Walk Hypothesis. Stock market indices.
Index funds versus mutual funds versus hedge funds.
Introduction to Modern Portfolio Theory. Diversification. Beta.
Derivatives contracts. Options and futures markets. Stock index futures.
Hedge Fund strategies: directional, long-short, arbitrage, event driven, etc.
Investing in Hedge Funds. Hedge Fund selection. Performance evaluation.
Properties of the normal distribution. Excel's statistical functions.
Random sampling and sampling distribution of the mean. Estimators.
Confidence intervals and hypothesis testing. Statistical inference.
Ordinary least squares (OLS). Regression analysis in Excel.
Financial applications: Analyzing asset prices in Excel. Pivot Tables. Histograms.
Financial applications: Statistical properties of stock returns. Non-normality. Fat tails.
Financial applications: Estimating Volatility and Correlation. Heteroscedasticity.
Financial applications: financial time series. Autocorrelation. Forecasting.
Some advanced functions Excel. Goal Seek and Solver. Data Tables.
VBA basics: the VBA editor. Recording and executing macros.
Sub and Function Procedures. Conditional statements. Loops.
Object browser. Immediate and Watch windows. Debugging a macro.
Financial applications: Tossing coins and rolling dice. Fair games. Martingales.
Financial applications: Random number generation. Simulating log-normal prices.
Financial applications: Simulating non-normal distributions (Poisson, Power law)
Financial applications: Monte Carlo simulation and option pricing.