Basics
Office hours: Monday and Tuesday, 3:00 - 4:00 pm.
Assigned Text: `Mathematics for Finance:
An Introduction to Financial Engineering'
Marek Capinski and Tomasz Zasawniak. Second edition.
Important dates
Monday (01/11/2016) First class.
Monday (03/01/2016) First midterm
Wednesday (03/02/2016) Middle of Semester. Last day to drop a course without a grade being reported.
Monday (04/13/2016) Second midterm
Friday (04/29/2016) Last day of classes.
Thursday (05/05/2016) 12:45pm - 2:45pm, Final Exam, Location: A332 Wells Hall
This and much more on the course Syllabus as a pdf
Schedules, Course materials, etc.
Class notes
Introductory Notes.
Prerequisite Review - including Probability, ODEs, Linear Algebra. 1/11 - 1/27.
Lecture 1 notes. Simple interest, Compound interest. 1/27.
Lecture 2 notes. Risk free contracts. Annuities, Perpetuities. 1/30.
Lecture 3 notes. Continuous compound interest. Effective interest. 2/1.
Lecture 4 notes. Coupon Bonds. 2/3.
Lecture 5 notes. Risky Securities, Introduction. 2/6.
Lecture 6 notes. CAPM, 2 securities. 2/8.
Lecture 7 notes. CAPM, n > 2 securities. 2/10 + 2/13.
Lecture 8 notes. CAPM, n securities + Bond. 2/13 + 2/15.
Lecture 12 notes. Introduction to Options. 2/24.
Lecture 13 notes. Regularity of Call + Put. 2/27.
Lecture 14 notes. Option Strategies. 3/1.
Lecture 15 notes. American Options. 3/3.
Lecture 16 notes. Introduction to Arbitrage. 3/13.
Lecture 17 notes. Options for the one step Binomial model. 3/15.
Lecture 18 notes. Options for the N step Binomial model. 3/17 - 3/22.
Lecture 19 notes. Scaling N step Binomial model to the continuum. 3/24.
Lecture 20 notes. Introduction to Browian motion. 3/27.
Lecture 21 notes. Introduction to Ito calculus. 3/29.
Lecture 22 notes. Examples of SDE's. 3/31.
Lecture 23 notes. Black Scholes for European Options. 4/3 + 4/5.
Lecture 24 notes. Solution of Black Scholes for European Call + Put. 4/7.
Lecture 25 notes. American Put - binomial model. 4/10.
Lecture 26 notes. Martingales and Optional Sampling for the American Put. 4/12.
Lecture 27 notes. Pricing the Perpetual American Put. 4/14.
Homeworks
Homework 1 (Due Wed 2/1) Sigma Algebra. PDF + CDF.
Joint distribution. Marginal and Conditional distributions. Solutions
Homework 2 (Due Wed 2/8) CLT. Simple interest, Compound interest. Solutions
Homework 3 (Due Wed 2/15) Bonds/Coupon Bonds. CAPM 2 securities. Solutions
Homework 4 (Due Wed 2/22) CAPM, 3 securities. Solutions
Homework 5 (Due Fri 3/17) Forwards.
(Quiz : Wed 3/22) Solutions correction
Homework 6 (Due Wed 3/22) Options.
(Quiz : Mon 3/27) Solutions
Homework 7 (Due Wed 3/29) Binomial model multistep. (Quiz: Mon 4/3) Solutions
Homework 8 (Due Wed 4/5) Ito Calculus. (Quiz: Mon 4/10) Solutions
Computational Project:
The project is to estimate prices of some options we have been studying this semester:
Assignment (Due Wed 4/26)
I expect you to write your own code and turn in your own assignment, but you can work alongside others to do this assigment.
You can program in any language you choose, include your code when you turn in the assignment.
Make sure your code is neat and well annotated.
You can find some nice sample code here srdas.github.io/Papers/cython.pdf for the European and American options.
(Note this code is in python. Python is free and relatively easy to use.
This code also uses numpy a numerical package for python that helps you with matrices etc.
Python(x,y) includes all this, you can get it here python-xy.github.io/ )
For the Asian option, I recomend you carry out a Monte-Carlo approach.
That is, simulate the change in the stock value with a sequence of coin flips
- average over many trials to estimate the value.
Note convergence to the proper value will be on the order of 1/[♯ of trials]
Here is a discussion of sample results Demo
Exam Review
Exam 1. (Wed 3/1) Covering homeworks 1 - 4. Review. formula sheet
Exam 2. (Mon 4/24) Covering homeworks 5 - 8.Review. formula sheet
Final. (Thursday, May 4 2017 12:45pm - 2:45pm in A332 Wells Hall) Covering all homeworks Review