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

Last modified: April 28, 2013, 09:11        Bookmark and Share