In-Class Material

These are the handouts distributed in print in class. Each one summarizes the material covered in that session and ends with practice problems.

Class	Date	Material Covered
Class 1	10/20	Probability spaces, random variables, linear combinations, joint and marginal distributions, conditioning and independence, conditional expectation, filtrations
Class 2	10/22	Densities and distribution functions; uniform, exponential, gamma, normal, lognormal and bivariate normal distributions; heavy tails
Class 3	10/27	Probability, moment and cumulant generating functions; sums, random sums and the Poisson limit; characteristic functions and the central limit theorem
Class 4	10/29	The gambler’s problem: probability of winning and expected duration of the game, with fair and biased coins
Class 5	11/3	Martingales, betting strategies, stopping times, the optional stopping theorem, ruin probabilities
Class 6	11/5	Poisson processes: waiting times, martingales and quadratic variation, superposition and thinning, compound Poisson processes, credit spreads and insurance ruin
Class 7	11/10	Brownian motion as the limit of random walks, its martingales, hitting a barrier, quadratic variation
Class 8	11/12	Trading gains and the Itô integral, Itô processes, Itô’s formula
Class 9	11/17	Correlated Brownian motions, Itô’s formula for two processes, Girsanov’s theorem
Class 10	11/19	Geometric Brownian motion: solution, distribution and moments of the stock price, expected return and growth rate, functions of the stock price
Class 11	11/24	Stochastic discount factors, dividends and the money-market account, the pricing equation in continuous time
Class 12	12/1	The risk-neutral measure; bonds, futures and forwards; Black-Scholes formula and PDE; the Merton model; jumps, credit spreads and option pricing with jumps

The normal distribution table is also distributed in class.