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Math 480B - Stochastic
Calculus for Option Pricing - Spring 2013
I plan to start with a derivation of the Black-Scholes
formula. The rest of the quarter will be devoted to
Brownian motion, stochastic
analysis and applications to mathematical finance.
- Time: MWF 11:30
- Room: LOW 102
- Instructor: Krzysztof Burdzy
- Office hours: W 12:30-2:20 or by appointment.
- Office: Padelford C-530, tel. 543-4297
- E-mail: burdzy@math.washington.edu
- Texts (optional):
`Introduction to the Economics of
Mathematics of Financial Markets' by
Jaksa Cvitanic and Fernando Zapatero,
`Stochastic Calculus for Finance', vol. I and II, by
Steven Shreve
- Grading policy: Midterm I 30%, Midterm II 30%,
Final 40%.
Exam rules: You may consult the textbooks and any other printed (published)
books. You may use your own class notes.
You may not use any other materials, for example, provided by
other people or found on the Web.
You may not discuss the problems with anyone else.
Midterm I
- Midterm solutions are due in class on ???.
- Material covered by Midterm I:
all material up to
and including the Ito formula ???
Midterm II Posted online: ???.
- Midterm solutions are due in class on ???.
- Material covered by Midterm II:
all material up to
and including the stochastic analysis derivation of Black-Scholes formula ???
Final Posted online: ???.
- The final is due on ???. Put the final in a sealed envelope in my mailbox in the "Math Lounge" on the first floor of Padelford Hall ???.
Homework
| Cvitanic and Zapatero |
| Topic
|
Page |
Problems |
Date due |
| Tree models | 98 |
2, 3, 4, 5, 6, 7 | April 8 |
| Replicating portfolio | 98 |
19, 20(a), 21, 22, 23, 26, 27, 28, 29 | April 8 |
| Option pricing | 268 |
1, 2, 3, 4 | April 8 |
| Black-Scholes | 268 |
9, 10, 11, 13 | April 15 |
| Arbitrage | 213 |
1, 2, 7, 9, 10, 11 | April 15 |
| Ito formula | 98 |
9, 10, 11, 12, 13, 14, 15, 16 | May 1 |
| Ito formula | 268 |
35 | May 1 |
| Option pricing | 268 |
6, 7, 25, 26, 27, 28, 29 | |
| Shreve I |
| Topic
|
Page |
Problems |
Date due |
| Tree models | 20 |
1.1, 1.2, 1.3, 1.5, 1.6, 1.7, 1.8 | April 8 |
| Tree models | 54 |
2.2, 2.8 | April 8 |
| Tree models | 83 |
3.3 | April 8 |
| Shreve II |
| Topic
|
Page |
Problems |
Date due |
| Brownian motion | 117 |
3.2, 3.4, 3.5, 3.6, 3.8 | April 29 |
| Stochastic calculus | 189 |
4.1, 4.2, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.13, 4.15, 4,16,
4.17, 4.18 | May 1 |
| Risk neutral pricing | 251 |
5.1, 5.2, 5.3, 5.8, 5.10, 5.12, 5.13 | |
| PDE's | 283 |
6.1, 6.2, 6.4, 6.5, 6.6, 6.8, 6.9 | |
Reading
| Cvitanic and Zapatero |
| Topic
|
Textbook section |
Pages |
Date due |
| Financial markets | Chapter 1 |
3-29 | April 3 |
| Tree models | 3.1-3.2 |
33-40 | April 3 |
| Black-Scholes via binomial model | 7.1-7.2 |
217-227 | April 8 |
| Brownian motion | 3.3.2 |
63-65 | April 15 |
| Stochastic integrals | 3.3.3-3.3.4 |
66-68 | April 22 |
| Ito formula | 3.3.5, 3.7 |
69-73, 94-101 | April 22 |
| Conditional expectations | 16.5 |
474-476 | April 22 |
| Martingale measure | 6.3.1, 6.3.6 |
188-192, 197-201 | |
| Feynman-Kac, Black-Scholes (PDE) | 6.3.7-6.3.8, 7.2 |
201-203, 220-227 | |
| Completness | 3.6.5-3.6.6 |
88-94 | |
| Shreve I |
| Topic
|
Textbook section |
Pages |
Date due |
| Tree models | Chapter 1 |
1-20 | April 3 |
| Shreve II |
| Topic
|
Textbook section |
Pages |
Date due |
| Brownian motion | Chapter 3 |
83-98 | April 15 |
| Stochastic calculus | Chapter 4 |
125-172 | April 22 |
| Risk-neutral pricing | Chapter 5 |
209-234 | |
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