# MATH 492 A: Stochastic Calculus for Option Pricing

Meeting Time:
MWF 11:30am - 12:20pm
Location:
SMI 407
SLN:
17145
Joint Sections:
STAT 492 A
Instructor:
Krzysztof Burdzy

### Syllabus Description:

Stochastic Calculus for Option Pricing

Winter 2020

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.

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 Posted online: February 7

• Midterm solutions are due in class on February 14.
• 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 .
• Extra office hours:

### Homework

 Cvitanic and Zapatero Topic Page Problems Date due Tree models 98 2, 3, 4, 5, 6, 7 Jan 22 Replicating portfolio 98 19, 20(a), 21, 22, 23, 26, 27, 28, 29 Jan 22 Option pricing 268 1, 2, 3, 4 Jan 22 Black-Scholes 268 9, 10, 11, 13 Jan 22 Arbitrage 213 1, 2, 7, 9, 10, 11 Jan 22 Ito formula 98 9, 10, 11, 12, 13, 14, 15, 16 Feb 10 Ito formula 268 35 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 Jan 22 Tree models 54 2.2, 2.8 Jan 22 Tree models 83 3.3 Jan 22

 Shreve II Topic Page Problems Date due Brownian motion 117 3.2, 3.4, 3.5, 3.6, 3.8 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 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

 Cvitanic and Zapatero Topic Textbook section Pages Date due Financial markets Chapter 1 3-29 Jan 6 Tree models 3.1-3.2 33-40 Jan 6 Black-Scholes via binomial model 7.1-7.2 217-227 Jan 6 Brownian motion 3.3.2 63-65 Jan 27 Stochastic integrals 3.3.3-3.3.4 66-68 Jan 27 Ito formula 3.3.5, 3.7 69-73, 94-101 Jan 27 Conditional expectations 16.5 474-476 Jan 27 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 Jan 6

 Shreve II Topic Textbook section Pages Date due Brownian motion Chapter 3 83-98 Jan 27 Stochastic calculus Chapter 4 125-172 Jan 27 Risk-neutral pricing Chapter 5 209-234
Catalog Description:
Introductory stochastic calculus mathematical foundation for pricing options and derivatives. Basic stochastic analysis tools, including stochastic integrals, stochastic differential equations, Ito's formula, theorems of Girsanov and Feynman-Kac, Black-Scholes option pricing, American and exotic options, bond options. Prerequisite: minimum grade of 2.0 in either STAT 395/MATH 395, or a minimum grade of 2.0 in STAT 340 and STAT 341. Offered: jointly with STAT 492.
GE Requirements:
Natural World (NW)
Credits:
3.0
Status:
Active
Last updated:
December 13, 2019 - 9:40pm