This page lists the courses I’ve taught at various universities.
This page lists the courses I’ve taught at various universities.
The main focus of this course is to understand the basics of arbitrage free pricing, and the mathematical tools used to price securities. We will begin with a rapid introduction to the multi-period Binomial model, and then mainly focus on continuous time markets. The mathematical tools we will use include conditional expectation, martingales, Brownian motion, Itô integrals and Itô's formula, exponential martingales, the Girsanov theorem and risk neutral measures. The course will cover the Black-Scholes option pricing model in detail, and may touch upon the fundamental theorems of asset pricing.
This course uses stochastic calculus to develop models for equity and fixed income derivatives. The role and limitations of risk-neutral pricing will be discussed. Both risk-neutral and forward measures will be used, and change of measure associated with change of currency will be explained.
This course introduces the most important securities traded in fixed income markets and the valuation models used to price them. Payoff characteristics and quotation conventions will be explained for treasury bills and bonds, STRIPS, callable bonds, mortgage-backed securities, and derivative securities like swaps, caps, floors, swaptions, and options on bonds. Basic concepts will be explained such as the relation between yields and forward rates, duration, convexity, and factor models of yield curve dynamics. Key concepts for interest rate derivative valuation will be introduced using discrete time versions of the Ho-Lee and Black-Derman-Toy models.
Basics of continuous-time stochastic processes. Wiener processes. Stochastic integrals. Ito's formula, stochastic calculus. Stochastic exponentials and Girsanov's theorem. Gaussian processes. Stochastic differential equations.
A friendly introduction to statistical concepts and reasoning with emphasis on developing statistical intuition rather than on mathematical rigor. Topics include design of experiments, descriptive statistics, correlation and regression, probability, chance variability, sampling, chance models, and tests of significance.