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# The solution has subtracting the rst equation from

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Unformatted text preview: ion has (subtracting the ﬁrst equation from the second): 25 = 100x ⇒ x = 1 Substituting in, we also get y = − 8 1 4 Binomial Stock Example I (continued) So we see we have the replicating portfolio: 1 4 150 × 50 - 1 8 × 100 100 = So we must have C0 = Jump to Method #2 1 1 × 100 − × 95 = \$13.125 4 8 Jump to Method #3 25 0 Expressing the Time-value of Money We could state the discount rate in a few ways: 1 90 2 100 100 The annualized interest rate (with no compounding) is 11.11% 100 111.10 111.10 The price of a 1-year zero coupon bond with face value \$1 is 1/1.111 = 0.90 3 The continuously compounded rate is − log(.9) = 10.54%, so that the price of a 1-year zero coupon bond is e −.1054 = 0.90. Hull uses the last method. For now, all we need is the price of the zero coupon bond, so I use the ﬁrst method. One-period Binomial Model Assumptions: Binomial price movement Frictionless market (no cost for buying or selling) Bd < 1 < Bu (Why do we need this?) Notation: S0 : initial stock price S0 u : stock price if it goes up S0 d : stock price if it goes down B : present value of \$1 in the future If you don’t like B , use 1 1+r instead Basic Idea of Pricing: ﬁnd a replicating portfolio, and use the no arbitrage argument Option Delta Deﬁnition Number of shares needed to replicate one call option is called hedge ratio or option del...
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## This document was uploaded on 10/28/2013.

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