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1. Let X (4, 9). Find:
(a) P (X < 5)
Solution.
Nomralizing X , we get,
Z=
54
= 0.11
9
Then,
P (X < 5) = P (Z < 0.11)
=
0.5438
(b) P (X > 2)
Solution.
Nomralizing X , we get,
Z=
24
= 0.22
9
Then,
P (X > 2) = 1 P (Z < 0.22)
= 1 (1 (0.22)
=
(0.2
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12.3. A companys cash position, measured in millions of dollars, follows a generalized Wiener process with a
drift rate of 0.5 per quarter and a variance rate of 4.0 per quarter. How high does the companys initial cash
position have to be for
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1. Determine the price of the four possible types of option for the following data:
S0 = 50, T = 1 year, K = 52, r = 10%, = 40%, n = 10
See Following Sheets.
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2. On the right side of t
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1. The cost of living is increasing at 10% per year in annual compounding.
(a) By what percentage will the cost of living increase in 3 years?
Solution.
Given,
r = 0.1
t=3
Now, assuming that the cost of living is P , the amount after three yea
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1.5. An investor enters into a short forward contract to sel1 100,000 British pounds for US dollars at an
exchange rate of 1.4000 US dollars per pound. How much does the investor gain or lose if the exchange rate at
the end of the contract is
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9.2. What is a lower bound for the price of a 4-month call option on a non-dividend-paying stock when the
stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum?
Solution.
In the question we are given,
S0
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1
10.4. Call options on a stock are available with strike prices of $15, $17 2 , and $20, and expiration dates in 3
1
months. Their prices are $4, $2, and $ 2 , respectively. Explain how the options can be used to create a buttery
spread. Cons
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1. Prove that
p D + KerT S0
Proof.
Rewriting the equation, we have,
p + S0 D + KerT
Now we have two portfolios,
Portfolio A: p + S0
Portfolio B: D + KerT
Now, there are two possibilities after time period, T ,
Case 1: ST < K
In this case, the
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1. A stock price is currently $60 and it is known that in three months it will be $70 or $55. The risk-free
interest rate is zero. Find the value of
(a) Three-month European call option with strike $62.
Solution.
Here we are given a strike pri