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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
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

Reading

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
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