Math 194
The Mathematics of Finance
Winter 2020
In this course we examine the mathematics of some of the basic derivative securities
encountered in financial markets. A prototype for such a derivative is the European put option, which is a contract giving its owner the right (but not the obligation) to sell a share of a specific stock at a fixed price (the strike price) on a fixed date. The buying of such an option provides the owner with a hedge against some of the risk associated with owning the stock---if on the fixed date the price of the stock exceeds the strike price, the option is worthless, but if the stock price falls below the strike price, the owner can exercise the option and sell the stock at a better-than-market price.
Economists R. Merton and M. Scholes won the Nobel Prize for their work on pricing such European put (and call) options, when the stock price is modeled by an exponential Brownian motion. (Scholes' collaborator F. Black died before the Nobel was awarded; Merton refined and extended the early work of Black and Scholes.)
In this course we will study a discrete version of the Black-Scholes-Merton (BSM) model, the Cox-Ross-Rubinstein (CRR) model. The mathematics of the CRR model is simpler than that needed for the
BSM model, but all of the key ideas necessary for the analysis are present in our analysis of the CCR
model. The model and its analysis are based on probability theory learned in Math 180A, and will also make use of linear algebra (Math 20F) and differential equations (Math 20D) learned in prerequisite courses.
- We will be using the first three chapters of the text
Introduction to the Mathematics of Finance by R.J. Williams.
- Lectures will be on Monday, Wednesday, and Friday, from 3 PM to 3:50 PM, in Center Hall 115.
- The discussion sections meet on Mondays according to the following schedule:
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Section A01: 6 to 6:50 PM, Center 203
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Section A02: 7 to 7:50 PM, Center 203
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Section A03: 7 to 7:50 PM, APM B402A
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Section A04: 8 to 8:50 PM, APM B402A
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Section A05: 7 to 7:50 PM, WLH 2115
- Your course grade will be based
on your performance on the two midterm exams and the
final exam. These
exams will be weighted as follows:
- Midterm 1: 25%
- Midterm 2: 25%
- Final: 35%
You will have the option of substituting your final exam score foroneof your midterm scores.
- There will be NO MAKEUP EXAMS given.
- In addition there will be weekly homework assignments which in total will account for
the remaining 15% of your grade. The assignments (and eventually their solutions) will be posted on this website.
Solutions should be clear and cogent, and neatly presented.
These assignments will be due on Tuesdays at 6PM.
- You will be submitting your homework assignments through GRADESCOPE.
- Your login is your university email address, and your password can be changed (or set) here.
- Your homework solutions should be in a single pdf file before being uploaded, or as a picture for each question.
- Please make sure your files are legible before submitting them — unreadable solutions will not earn credit.
- Most word processors can save files as a pdf.
- There are many tools to combine pdfs, such as this one, and others for turning jpgs into pdfs, such as this one.
- The midterm exams will be given in class on January 31 and February 28 (Friday of fourth and eighth weeks).
- The final exam is scheduled for Wednesday, March 18, from 3:00 PM to 6:00 PM.
- The +/- grading system will be used for course grades.
- TURN OFF cell phones in lecture, discussion sections, and exams.
- Academic Integrity is highly valued at UCSD and academic dishonesty is considered a serious offense.
Occurrences of academic dishonesty will be reported to the Academic Integrity Office. Students involved in an academic integrity violation will face administrative sanctions which may include suspension or, in very serious cases, expulsion from the university. Cultivate and protect your academic integrity! For more about academic integrity and its value, visit the UC San Diego Office of Academic Integrity.
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January 2, 2020