10.40

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8 Answers

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10.40

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Calculate first the risk neutral probability.

(I.e you are assuming the current stock price is efficiently priced in)

With the stock price tree, risk neutral probability Pi:

Its $10 = pi * $12 + (1-pi)*$8

Solving for Pi = 0.5

Then to calculate the value of call:

Substitute Pi with the payoffs ($2 = $12 - 10 and $0 as option is worthless at <$10)

C(0) = (pi*($2) + (1pi)*$0 )/ r

= 0.5 * 2

= $1 (Since r = 1, 0 interest rate)

A normal expected value of the option (non risk neutral) will just be 0.6*$2 + (0.4)*$0 = $1.2.

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$1

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Expectation under any measure is equivalent. That's why we change measures to calculate things as the result will be same. Answer is 1

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Can someone explain why the answer is 1 and not 1.2:?

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Jim, because you get 1.2 with physical probabilities, and 1 with risk neutral probabilities. To use the binomial tree pricing approach you should use the risk neutral probabilities. Th calculations are provided above.

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First compute risk neutral prob.