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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
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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
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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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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 th
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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 l
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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%
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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 t
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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 a
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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 wi