Mathematics for Finance

Math 4412

Fall 11

 

 

 

Class Logistics

Venue: A-2 Academic Block

Timings: T-R, 6-8 pm

 

Course Outline

Mathematics for Finance

 

Exams

Exam I

Exam II

 

Lectures

The books referred to in suggested readings are

CZ: Capinski. M & Zastawniak. T, Mathematics for Finance, Springer 2003

DH: Higham. D, An Introduction to Financial Option Valuation, Cambridge University Press 2004

PW: Wilmott. P, Paul Wilmott on Quantitative Finance, Wiley 2006

SS: Shreve. S.E, Stochastic Calculus for Finance I & II, Springer 2000

Lecture 1 - Introduction to Discrete Time Finance Models

Readings: C&Z - Chapter 1

DH - Chapter 1

Lecture13 -  Monte Carlo Simulations using MATLAB

Readings: DH - Chapter 4

 

Lecture 2 - Probability on Discrete Spaces I

Readings: DH - Chapter 3

SS -  Chapter 2

Chapter 1: Stochastic Processes and the Mathematics of

Finance by J. Block

 

Lecture14 (Extra) - Forwards and Futures

Readings: C&Z - Chapter 6

 

Lecture 3 - Probability on Discrete Spaces II

Readings: DH - Chapter 3&4

SS - Chapter 2

Chapter 3: Stochastic Processes and the Mathematics of

Finance by J. Block

 

Lecture15 -  Probability on Continuous Spaces I

Readings: Chapter 1: Stochastic Processes and the Mathematics of

Finance by J. Block

 

Lecture 4 - Simple Interest, Periodic Compounding, Annuities and Perpetuities

Readings: C&Z - Chapter 2

PW - Chapter 1

 

 

Lecture16 - Probability on Continuous Spaces II

Readings: SS (Vol. II) - Chapter 2,3

PW - Chapter 4

Lecture 5 - Compounding Methods, Bonds & Bond Valuation

Readings: C&Z - Chapter 2

PW - Chapter 1

Prof. Robert's (Wharton) Global Finance Lecture Notes - Bond Valuation

 

 

Lecture17 - Ito Stochastic Calculus

Readings: DH - Chapter(s) 5,6 & 7

PW - Chapter 4 SS (Vol. II) - Chapter 4

 

Lecture 6 - Risky Assets: Stocks & Binomial Model

Readings: C&Z - Chapter 3

SS - Chapter 1

DH - Chapter 4

 

Lecture18 - Black Scholes Equation and it's Variants

Readings: DH - Chapter 8

PW - Chapter 5, 8

 

Lecture 6 - Risky Assets: Stocks & Binomial Model

Readings: C&Z - Chapter 3

SS - Chapter 1

DH - Chapter 4

 

Lecture19 - Solving the Black Scholes Equation I

Readings: DH - Chapter 8

PW - Chapter 6

Black. F and Scholes. M, The Pricing of Options and Corporate Liabilities

 

Lecture 8 - Portfolio Theory I

Readings: C&Z - Chapter 5

Markowitz. H: Portfolio Selection

Lecture20 - Solving the Black Scholes Equation II

Readings: DH - Chapter 18

PW - Chapter 9

Derman E. and Taleb N., The Illusions of Dynamics Replication

Wilmott P., In defense of Black, Scholes and Merton

 

Lecture 9 - Portfolio Theory II & CAPM

Readings: C&Z - Chapter 5

Markowitz. H: Portfolio Selection

 

Lecture21 - Interest Rate Derivatives

Readings: PW: Chapter 32

 

Lecture10 - Introduction to Options

Readings: C&Z - Chapter 7

PW - Chapter 2

DH - Chapter 1

Lecture22 - Finite Difference Schemes for PDE

Readings:

 

Lecture11 - Option Pricing using the Binomial Model

Readings: C&Z - Chapter 8

SS - Chapter 1

Cox. J, Ross. S & Rubenstein. M: Option Pricing a Simplified Approach

Lecture23 - Finite Difference Schemes for the Black Scholes Equation

Readings:

 

Lecture12 -The CRR and Black Scholes Formulae

Readings: C&Z - Chapter 8

SS - Chapter 1

Higham. D: Nine Ways to Implement the Binomial Method for

Option Valuation in MATLAB

 

Lecture24 - Monte Carlo Methods

Readings:

 

 

 

Homework

Homework 1

Homework 2

Homework 3

Homework 4

 

MATLAB Stuff

MATLAB Tutorial I

MATLAB Tutorial II

MATLAB Tutorial III