ecg590i_lecture10

Ecg590i_lecture10 - ECG590I Asset Pricing Lecture 10 Binomial Trees 10 10.1 Binomial Trees One-step model 1 Model structure John Seater North

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ECG590I Asset Pricing. Lecture 10: Binomial Trees 1 10 Binomial Trees 10.1 One-step model 1. Model structure John Seater, North Carolina State University, Fall 2007
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ECG590I Asset Pricing. Lecture 10: Binomial Trees 2 There is only one time interval ( t 0 ; t 1 ) There are only two possible outcomes for S High, with probability p Low, with probability 1 ± p In the diagram above, Low is shown below Initial and High is above Initial, implying that one of the outcome is an increase in value and the other is a decrease. In general however, both outcomes could be increases or decreases. We study the general model later. John Seater, North Carolina State University, Fall 2007
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ECG590I Asset Pricing. Lecture 10: Binomial Trees 3 2. Pricing a call option: numerical example (a) Setup The risk-free rate is r = 0 : 25 K = 45 . John Seater, North Carolina State University, Fall 2007
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ECG590I Asset Pricing. Lecture 10: Binomial Trees 4 (b) Notice that S 0 does not equal the discounted expected value of S 1 : S 0 = 32 < 1 1 + r E [ S 1 ] = 1 1 + 0 : 25 [ p 60 + (1 ± p ) 30] = 4 5 1 2 60 + 1 2 30 ± = 36 John Seater, North Carolina State University, Fall 2007
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ECG590I Asset Pricing. Lecture 10: Binomial Trees 5 (c) Pricing the call: riskless portfolio method Consider the following portfolio: Long shares of stock Short one call Find the value of that makes the portfolio riskless If the stock rises to 60, the portfolio is worth ± 15 If the stock falls to 30, the portfolio is worth . To be riskless, the portfolio must have the same value for either
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This note was uploaded on 10/05/2009 for the course ECG 590 taught by Professor Msmorril during the Fall '08 term at N.C. State.

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Ecg590i_lecture10 - ECG590I Asset Pricing Lecture 10 Binomial Trees 10 10.1 Binomial Trees One-step model 1 Model structure John Seater North

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