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# PPT 5 - 5 Binomial Tree Model Reading Chapter 12 Chapter 11...

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5. Binomial Tree Model Reading: Chapter 12, Chapter 11 of Luenberger 1

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5.1 A Toy Model That Could Later Be Made Very Realistic Suppose a stock is currently at price S. In a later time t, it could move up and down, but only to one of the two known states: We do not know the probability p that the stock will go up, or ( 1-p ) that it will go down. So the stock price at t is random . Is there a way to calculate p? How do we value a call option C at t=0 ? 2 or , 0. Su Sd u d
How to make the toy model more realistic (Chapter 11; will not cover in detail here) Make t very small, and attach many t s one after the other. Small fixed bistate changes in each t can add to yield any value of change in a stock price at larger time intervals. We can match the historical volatility of this stock with the volatility of the binomial tree model to yield 3 and t t u e d e

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