# A2 buy one share at time 1 if the stock is at 120 and

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: to buy the stock (but not an obligation to do so) for 100 at time 1. If the stock price is 80, you will not exercise the option to purchase the stock and your proﬁt will be 0. If the stock price is 120 you will choose to buy the stock at 100 and then immediately sell it at 120 to get a proﬁt of 20. Combining the two cases we can write the payo↵ in general as (X1 100)+ , where z + = max{z, 0} denotes the positive part of z . Our problem is to ﬁgure out the right price for this option. At ﬁrst glance this may seem impossible since we have not assigned probabilities to the various events. However, it is a miracle of “pricing by the absence of arbitrage” that in this case we do not have to assign probabilities to the events to compute the price. To explain this we start by noting that X1 will be 120 (“up”) or 80 (“down”) for a proﬁt of 30 or a loss of 10, respectively. If we pay c for the option, then when X1 is up we make a proﬁt of 20 c, but when it is down we make c. The last two sentences are summarized in the following tab...
View Full Document

## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

Ask a homework question - tutors are online