Outcomes one through five in a single-period framework correspond to elements in the
following probability vectors that exist in and in spaces:
= [0, .1, .21, .29, .4] T
= [0, .4, .3, .2, .1] T
Thus, for example, the probability of outcome 1 is zero under both and .
a. Are and equivalent probability measures?
b. If the current riskless return rate equals 10%, what is the current value of a put option on a
stock with the following payoff vector under these same 5-outcome risk-neutral measures
with : [20, 30, 40, 50, 60] T ? You should assume that the put has an exercise price equal
to 35.
c. Suppose that a futures contract trades on the stock in part b. What is the current futures
price on this contract?
d. Suppose that there is a call with an exercise price of 35 trading on the stock from part b.
What is the expected risk-neutral value of this call contingent on it being exercised?
e. Consider the stock for which the payoff vector is given in part b. If one were to use the
riskless one-year bond as the numeraire for pricing purposes, what would be the current
stock price under its equivalent martingale measure based on the equivalent probability
measure ? (Make sure that you denominate your final numerical answer in terms of
either the correct number of dollars or riskless bonds.)
