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Stock: S0 = 1.5 1.05S0 u
1.05S0 d This is exactly like if it were a stock with price S0 , S0 u , S0 d and it
paid a dividend out that was 5% of the future price. Option on a currency (continued) So to compute the option price we can solve for q :
1.6 = 1
(1.05 × q × 1.7 + 1.05 × (1 − q ) × 1.5)
1.03 Solving: q = 0.3476. Thus we can price the option:
Stock: C0 =??? C= 0.10
0 1
(q × (0.10) + (1 − q ) × 0) = 0.0338
1.03 Multiperiod Binomial Model
We can also extend our model to have multiple periods.
First, lets go through the twoperiod steps again and then add
another period.
Example. Valuation of a European call on a stock.
Current stock price is $50.
There is one period to go.
Stock price will either go up to $75 or go down to $25.
There are no cash dividends.
The strike price is $50.
one period borrowing and lending rate is 10%. A New Example The stock and bond present two investment opportunities:
50 75 1 25 The option’s payoﬀ at expiration is:
C0 25
0 1.1
1.1 Example (continued)
Question: Wha...
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This document was uploaded on 10/28/2013.
 Spring '13

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