# Options and Futures Mini, FIN 524

Philip H. Dybvig
Washington University in Saint Louis

Final Exam I can't believe the mini is over already. I have graded the exams, and I am happy to report that the distribution of performance is great. I still need to double-check my work and record the grades before the exams are returned to you. In the meantime, here are the exam and the answers:

...and here are the preliminary results:

score count
119 1
110-112 4
104-109 9
95-102 18
92-94 8
81-89 6
46 1

Most students got full credit for part A, got 4 or 5 of 5 on part B, and missed a few points on part C. My only slight disappointment was that only one student got part D almost completely correct, but I do have to admit it is a hard problem. Most commonly, people failed to take the average over times and used mu instead of r as the growth rate. In the risk-neutral probabilities, the stock price grows on average at r not at mu. I gave a lot of partial credit, especially to students who got a good chunk of the problem correct.

I wanted to mention that I counted off a tiny amount (one point) for misusing continuous compounding in Part C4. If we use continuously compounded interest in that part, we need to use the continuous interest rate c such that exp(-c)=1/1.25, i.e., c=log(1.25). If we use c=0.25, that is inconsistent with discounting in the earlier part and can create all sorts of strange and spurious results: a couple of times I have been paid good money to track down the source of a strange result that was due to this. In part C4 in the exam, the mispricing is significant (about \$2.50 per call), as it will typicially be if the interest rate times the time to maturity is large.

Once the exams have been returned, I will be happy to hear about serious mistakes but I will not be sympathetic if you complain about a couple of points here and there.

Welcome to Options and Futures! This course introduces the popular option pricing tools that have come to be used in all areas in finance. The concepts, tools and applications promise to make this a great term!

Site of the week! Do you think you will suffer financially if your favorite presidential candidate loses? Hedge your position on the Iowa Electronic Markets, where you can find digital options on various presidential outcomes.

Previous sites of the week

Practice Problems and Solutions

Lecture 1: Problems - Solutions

Lecture 2: Problems - Solutions

Lecture 3: Problems - Solutions

Lecture 4: Problems - Solutions

Lecture 5: Problems - Solutions

Practice exams

(I) Exam - Solution

(II) Exam - Solution

Slides

I recommend that you print a set of slides before class for taking notes and solving in-class exercises. One set of slides corresponds to one week (two classes) of lectures.

The condensed versions below shrink each slide to the corner to leave more room for taking notes. The regular pdf versions are the same as the slides used in class.

Lecture 1: Foundation
...pdf size 41K
...pdf condensed size 41K

Lecture 2: Binomial Option Pricing and Call Options
...pdf size 85K
...pdf condensed size 85K

Lecture 3: Put Options and Distribution-Free Results
...pdf size 89K
...pdf condensed size 89K

Lecture 4: The Black-Scholes Model
...pdf size 117K
...pdf condensed size 117K

Lecture 5: Forwards, Futures, and Futures Options
...pdf size 62K
...pdf condensed size 63K

week 6: wrap-up and review