Pricing Derivatives
89
Chapter 10
Pricing Derivatives
Contents
10.1 Pricing Risky Cash Flows .
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10.2 Pricing Derivatives
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10.3 Interpreting Equity as an Option
. . . . . . . . . . . . . . . . . . .
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10.1
Pricing Risky Cash Flows
We now want to use the methods for pricing future, uncertain cash Fows discussed
in chapter 8 to price derivatives. Consider a a security that promises a random
cash Fow
in the future, which equals either a high
or a low
.Th
eca
sh
Fows can be illustrated as
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✟
✟
✟
✟✯
❍
❍
❍
❍
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We want to ±nd the value
now of these uncertain, future cash Fows. The
general rule for pricing was
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Pricing Derivatives
where
and
are the current market prices for digital options that pay oF in
the two states. Alternatively we found the value as
where
is the risk free interest rate and
and
are time 1 prices of receiving
$1 in states
and
(also termed “state price probabilities”). Since
and
sum to one and are never negative, they behave like probabilities. One can
alternatively think of the calculation as “The expected payoF under the state
price probabilities,” and use the notation
to ±nd 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 de±nes 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 deFnes all
relevant
future states
for pricing a derivative security written on MNO stock.
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 Fall '08
 Lehmann,B
 Strike price, pricing derivatives

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