Unformatted text preview: r negative, they behave like probabilities. One can
alternatively think of the calculation as “The expected payoﬀ under the stateprice probabilities,” and use the notation to ﬁnd the following basic pricing formula:
(10.1) 10.2 Pricing Derivatives
This framework is perfect for pricing derivatives, since the values of the underlying
securities deﬁnes the relevant states.
Example
Stock MNO has price today ( ) of $98, and will next period either have a price of
or a price of
. These two mutually exclusive cases deﬁnes all relevant future states
for pricing a derivative security written on MNO stock. ✟
✟✟ ✟✟
❍
❍❍ ✯
✟
✟✟ ❍
❍❍ ❍
❥
❍ Pricing derivatives merely consist of ﬁnding the future cash ﬂows from the derivative as a function of the value of the underlying, and applying the same state price
probabilities in the basic pricing relation (10.1). The state price probabilities have
to be the same for all derivatives. This follows from the no arbitrage assumption
and will be discussed further in chapter 14. 10.2 Pricing Derivatives 91 Example
What is the price of an...
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This document was uploaded on 02/15/2014 for the course BEM 103 at Caltech.
 Fall '08
 Lehmann,B

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