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 knownstates: •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.SuSd ud
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 tcan 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 ttuede
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