Derivative Securities, Fall 2009

Course Details and Schedule


Multivariate calculus (partial derivatives, multiple integrals, Lagrange multipliers, etc.), linear algebra (linear equations, solvability, eigenvalues of symmetric matrices, bases for vector spaces), calculus based probability (probability density functions for univariate and multivariate random variables, conditional and marginal density by integration, the central limit theorem, the formulas for univariate and multivariate gaussian densities), some experience with computing (see below).


Some of the assignments will involve computation using Microsoft Excel and C++. Students need not have experience with Excel or C++, but they should have used some programming language, such as Matlab, C/C++, R, etc. Students will need access to Microsoft Excel. Experience shows that shareware substitutes such as Open Office do not function correctly enough for the purposes of this class. Students also will need access to a C++ compiler. This should be on the same computer that is running your Excel because you will need to create files with one and use them with the other. Students in Computing in Finance will be fine. Details are being worked out and will be announced shortly.


The final grade will be determined by the grades on the homework assignments and the final exam, each counting for about half the total. Homework grades will be posted on the nyuHome web site. Only registered students may submit homeworks for grading. There will be a penalty for assignments submitted late, which is an increasing but moderate and unspecified. Within reason, it is better to submit an assignment late but complete rather than on the due date but incomplete.


There is a message board at the nyuHome web site. Sign in with your NYU netid and password, then click on the "Academics" tab, then on the class "Derivative Securities" link (Warning: this will not work until you register for the class.), then the "Communication" button on the left, then (finally) the "Discussion board" link. Please post all academic questions or comments on the message board (questions about an assignment, answers to questions or other comments, announcements of study sessions, etc.). Always check the message board before working on an assignment, as there often will be corrections or hints. Please email an instructor or TA only for personal matters (schedule an appointment, request to submit an assignment late, etc.).


Students are encouraged to discuss homework exercises with each other. Each student must write the solutions himself or herself. Copying of solutions or allowing others to copy your solutions is considered cheating and will be handled according to NYU cheating policies. Code sharing is not allowed. You must type (or create from things you've typed using an editor) every character of code you use.

Weekly schedule (tentative)

Date Lecture topics Readings Due this class
Sept. 9 Futures, arbitrage and the forward price, settlement. Puts and calls, nonlinear returns, return distribution. Hull, chapters 1, 2, 3, 5 none
Sept. 16 Discrete models, complete markets, replication and arbitrage pricing. Multiperiod binomial model, rebalancing and dynamic replication. tba none
Sept. 23 Multiperiod hedging with a forward. Risk neutral process, equivalent martingale measure and pricing. Constructing a binomial tree to match a continuous process, volatility and expected return. tba HW1
Sept. 30 The continuous time limit, the lognormal random variable, the Black Scholes formula, implied volatility. Limitations of the Black Scholes model, volatility skew, smile, and term structure for equity and equity index options. tba tba
Oct. 7 All about the Black Scholes formula, asymptotic approximations, the "Greeks": Delta, Gamma, Rho, and Vega. Risk assessment and control for hedges and portfolios of options. Some empirical illustrations. tba tba
Oct. 14 Diffusion processes. Continuous time limits: random walk to Brownian motion, binomial tree to geometric Brownian motion. Drift, noise, and quadratic variation. Ito's lemma, Stochastic integrals and stochastic differential equations. tba tba
Oct. 21 Diffusion processes (continued). The backward equation and applications. The Black Scholes equation. Difference approximations for backward equations and their relation to binomial trees. tba tba
Oct. 28 Boundary conditions: barrier options, American style options, tree pruning. Pricing with a volatility surface or term structure. tba tba
Nov. 4 Bonds, bond and bond index futures, stripping and bootstrapping. Interest rate derivatives: swaps, swaptions, caps. The yield curve, its structure and variation. tba tba
Nov. 11 One factor short rate models. Their abstract theory: martingale measures and the market price of risk. Specific models: Vasicek, Hull-White, Ho-Li, and the yield curves they generate. tba tba
Nov. 18 Pricing interest rate derivatives, the PDE approach. Black's model and its (lack of) theoretical underpinnings. Yield curve modeling (briefly). tba tba
Nov. 25 Categories of credit risk: mortgages and bonds. Credit ratings and rating agencies. Credit default swaps, credit risk markets. Credit risk pricing, credit spreads. What happened last year. tba tba
Dec. 2 Pricing models for credit spreads and risk products. Merton's model of default. Historical and implied default probabilities. Default correlation, copulas, and implied correlation. tba tba
Dec. 9 Currencies and currency derivatives. tba tba
Dec. 23 Final exam, same time, same room