Syllabus and Assignments
Mathematics 16:642:622 - Spring 2007
Lecture Schedule and Homework Assignments: This page will record the topics we cover in each lecture, reading assignments, and homework assignments or projects, with links to lecture notes, homework assignments, solutions, and additional information as needed. Reading material from the texts on the reserve list is strongly suggested, but not absolutely necessary. Reading material from the class text and handouts is required. Students should study the reading assignments before class.
| Lecture | Topics | Reading Assignments | Homework Assignments |
|---|---|---|---|
| 1 |
Review of stochastic calculus; Markov processes, martingales; interest rate models and solution of SDEs |
Lectures 1 & 2 (pdf) Shreve II, §4.1-4.4, Examples 4.4.10, 4.4.11, 6.2.2, & 6.2.3 |
|
| 2 | Vasicek, Hull-White and CIR models; PDE for a zero-coupon bond price |
Shreve II, § 6.2, & 6.5 |
Homework 1 (pdf) Due 1/29/2007. Solutions |
| 3 |
Reflection principle; first passage time; Maximum of Brownian motion, without and with drift |
Lecture 3 (pdf) Shreve II, § 3.7, 7.1, 7.2 |
|
| 4 | Barrier options |
Lecture 4 (pdf) Shreve II, § 7.3 |
Homework 2 (pdf) Due 2/5/2007. Solutions |
| 5 |
Barrier options (continued), stopping times, maximum of Brownian motion |
Lectures 5 & 6 (pdf) Shreve II § 3.6, 3.7, 7.3 |
|
| 6 |
Stopped processes, Doob's Optional Sampling Theorem, barrier options and PDEs |
Shreve II, § 8.2, 7.3, 7.4;
Wilmott, pp 408, 409, 410, 411, 412, 413, 414, & 415 |
Homework 3 (pdf) Due 2/12/2007. Solutions |
| 7 | Lookback options and PDEs | Lectures 7 & 8 (pdf) Shreve II § 7.4.1-3 |
|
| 8 | Lookback options and closed-form formulae via probability |
Shreve II § 7.4.4, Willmott (2006) § 26 Wilmott, pp. 445-452 |
Homework 4 (pdf) Due 2/19/2007. Solutions |
| 9 | Asian options and PDEs | Lectures 9 & 10 (pdf) Shreve II § 7.5.1, 7.5.2, Willmott (2006) § 25 |
|
| 10 | American options; perpetual put | Shreve II § 8.1, 8.2, 8.3, Willmott (2006) § 9 | Homework 5 (pdf) Due 2/26/2007. Solutions |
| 11 | American options; finite-maturity put | Lectures 11 & 12 (pdf) Shreve II § 8.4, Jarrow & Turnbull, § 7 |
|
| 12 | American options; finite-maturity call | Shreve II § 8.5.1, Karatzas & Shreve, § 2.4, 2.5, 2.6 |
Homework 6 (pdf) Due 3/5/2007. Solutions |
| 13 | Forwards and futures | Lectures 13 & 14 (pdf) Shreve II § 5.6, 9.1; Hull § 2, 3, 5 |
|
| 14 | Change of numéraire and risk-neutral measure | Shreve II § 9.2 | Homework 7 (pdf) Due 3/19/2007. Solutions |
| Spring Break | No Lectures or Office Hours | No Class 3/12/2007 | |
| 15 | Forward measures; stochastic interest rates and Black-Scholes-Merton formula |
Lectures 15 & 16 (pdf) Shreve II § 9.4 |
|
| 16 | Foreign exchange market model; domestic and foreign risk-neutral measure |
Shreve II § 9.3.1, 9.3.2, & 9.3.3 | Homework 8 (pdf) Due 3/26/2007. Solutions |
| 17 | Affine yield interest rate models | Lectures 17 & 18 (pdf) Shreve II § 10.1, 10.2 |
|
| 18 | Affine yield interest rate models (continued), Heath-Jarrow-Morton model |
Shreve II § 10.2, 10.3 | Midterm (pdf) Due 4/2/2007 |
| 19 | Review of affine-yield and HJM models; Heath-Jarrow-Morton model implementation |
Lectures 19 & 20 (pdf) Shreve II § 10.1-10.3.5 |
Midterm exam solutions: Problems 1 & 3 (pdf) and Problems 2 & 4 (pdf) |
| 20 | Forward LIBOR model | Shreve II § 10.4.1-10.4.4 | Homework 9 (pdf) Due 4/9/2007. Solutions |
| 21 | Forward LIBOR model (continued); Caps, caplets, and Black caplet formula |
Lectures 21 & 22 (pdf) Shreve II § 10.4.4-5 |
|
| 22 | Forward LIBOR term structure model and calibration; Swaps, swaptions, and swap market model |
Shreve II § 10.4.6, Björk § 25, Brigo & Mercurio § 6.1-7 Notes on HJM and LIBOR market models (pdf) |
Homework 10 (pdf) Due 4/16/2007. Solutions |
| 23 | Swaps, swaptions, swap market model, and Black's formula for swaptions |
Lectures 23 & 24 (pdf) Björk § 25 (pdf), Brigo & Mercurio § 6.7 Expository paper on swaps |
|
| 24 | Introduction to jump models, Poisson, compound Poisson, and jump processes |
Shreve II § 11.1-4 | Homework 11 (pdf) Due 4/30/2007 |
| 25 | Stochastic calculus for jump processes | Lectures 25 & 26 (pdf) Shreve II § 11.5 |
|
| 26 | Change of measure for jump processes | Shreve II § 11.6 | Final (pdf) Due 5/7/2007 |
| 27 | Lectures 27 & 28 (pdf) | ||
| 28 | Final exam due 6:40pm Last class 5/7/2007 |
Links
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RAMS mailing list management for math622_spring2007 (at) rams.rutgers.edu (RCI login required)
Instructor homepage
Teaching Assistant homepage
Library reserve list
Library (RCI login required for off-campus electronic journal access)
Link to Spring 2006 Math 622 course webpage
Quantitative finance software
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