Concept Study Sheet
Midterm II
Math 174 Winter 2011
On examinations you are responsible for the content of readings, lectures and homework.
Use this guide to help you study the topics. It is more effective to study explicitly topic
by topic than to just reread the text.
Overview: we studied Chapters 11,12, 13, also reviewing in lecture some basic
probability concepts, esp. pertaining to the normal distribution. since the last midterm.
You will be tested this content.
The overall main topic is derivative pricing.
As last time, it is worthwhile to recall that many finance and probability concepts have
very good wikipedia articles on them; I recommend that you use this and other web
resources as you need them.
Chapter 11. One step binomial model. Be able to set up and solve a problem with
numbers. Be able to find the portfolio (stock plus cash invested or borrowed at rate r) that
replicates a given derivative. Be able to find the portfolio of stock and cash that is risk
free. (See below about Delta.) Be able to find the risk neutral measure. Be able to derive
and implement formulas 11.111.3. Be able to explain why the actual probability of u and
d moves is irrelevant to the price of the option. Make sure you understand
how the
pricing theory is built on the principle of no arbitrage. Be able to explain to show that in a
risk neutral world (one where the risk neutral measure gives the probability of u and d
moves), the expected value of the stock is given by 11.4. Be able to compute risk neutral
probability of p (of an up move) using this formula (i.e. by risk neutral valuation). Be
able to compute with
multiple step trees, and derive formulas 11.711.10, and their
generalizations to multiple steps. Be able to use binomial method to price puts and calls.
Be able to price American calls where at each node n you exercise early iff the value f_n
of the option at that node n is less than the payoff gotten from early exercise. Exercise: be
able to show in the onestep case that it is never optimal to early exercise an American
call. Show that this is not so for a put. Understand the quantity delta given by 11.1, i.e. it
is the number of shares of stock to hold for each option shorted, in order for the resulting
portfolio to be riskless. Be able to start from a given volatility sigma and compute the
CoxRossRubinstein values for u and d (and hence p) using 11.1311.16.
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 Spring '11
 DonBlasius
 Math, Normal Distribution, Variance, Probability theory, probability density function, Ito

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