Teaching

I have developed lecture notes and homework sets for a number of courses at the University of Washington. I am happy to make these available to anybody that wishes to use them. Homework solutions are also available on request.

CFRM 504: Options and Other Derivatives

This one-quarter course, intended for masters students in Computational Finance and Risk Management, introduces students to basic financial derivatives, explores how to price them, and how to use them to manage financial risk. Specific topics covered in the course include arbitrage, the 1st and 2nd fundamental theorems of asset pricing, the binomial, trinomial and Black-Scholes models, stochastic volatility, local volatility, European and American options, variance swaps and barrier claims.

Lecture notes can be downloaded here.

CFRM 530: Fixed Income Analytics

This one-quarter course, intended for masters students in Computational Finance and Risk Management, introduces students to basic interest rate derivatives, explores how to price and replicate them, and how to use them to manage financial risk. Specific topics covered in the course include short-rate models (in particular, affine term structure models), the Heath-Jarrow-Morton (HJM) forward rate framework, market models, and the pricing and hedging of interest rate derivatives in these settings.

Lecture notes can be downloaded here.

AMATH 561/562: Introduction to Probability and Stochastic Processes

This two-quarter course, intended for PhD students in Applied Mathematics, provides students with a broad introduction to measure-theoretic probability and stochastic processes. Specific tops covered in the course include probability spaces, random variables, conditional expectations, generating and characteristic functions, Markov chains in discrete and continuous time, branching processes, convergence of random variables, Brownian motion, Ito processes, stochastic calculus, stochastic differential equations and their connections to elliptic and parabolic PDEs, Levy processes, jump-diffusions, stochastic control, optimal stopping and Monte Carlo simulation.

Lecture notes can be downloaded here.