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BOCh10 - Pricing Derivatives 89 Chapter 10 Pricing...

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Pricing Derivatives 89 Chapter 10 Pricing Derivatives Contents 10.1 Pricing Risky Cash Flows . . . . . . . . . . . . . . . . . . . . . . . 89 10.2 Pricing Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . 90 10.3 Interpreting Equity as an Option . . . . . . . . . . . . . . . . . . . 92 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 ✟✯ ❍❥ We want to ±nd the value now of these uncertain, future cash Fows. The general rule for pricing was
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90 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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BOCh10 - Pricing Derivatives 89 Chapter 10 Pricing...

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