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ecg590i_lecture10 - ECG590I Asset Pricing Lecture 10...

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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 ° The call option°s strike price is 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 ² 60 + (1 ± p ) ² 30] = 4 5 ° 1 2 60 + 1 2 30 ± = 36 Presumably, this fact re±ects risk aversion. 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 60° ± 15 ° If the stock falls to 30, the portfolio is worth 30° . ° To be riskless, the portfolio must have the same value for either outcome: 60° ± 15 = 30° ) ° = 1 = 2 ° Value of this riskless portfolio at t 1 : 15 John Seater, North Carolina State University, Fall 2007
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ECG590I Asset Pricing. Lecture 10: Binomial Trees
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  • Fall '08
  • msmorril
  • North Carolina State University, North Carolina State, Carolina State University, John Seater, ECG590I Asset Pricing

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