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Unformatted text preview: ke place: the
“up”node. The price is
1
1
1
×
×
× (0.055 − 0.05) × 1000 = 2.26.
2 1.05 1.055
Part III. MULTIPLE CHOICE QUESTIONS
Please note your answers on the front page.
1. Consider the following binomial interestrate tree modeling the future evolution of annual
continuously compounded interest rates. The periodlength is one year. 0.06 0.055 0.05 0.05 0.045 0.04 The riskneutral probability is given to be equal to 1/2. What is the price of a zerocoupon
bond redeemable in three years for $1,000?
(a) $814.85.
(b) $860.72.
(c) $898.78.
(d) $904.85.
(e) None of the above. 7 Solution: (b)
The price of a onedollar, zerocoupon bond is
P0 (0, 3) = e−0.05 × 1
× (e−0.045 (e−0.04 + e−0.05 ) + e−0.055 (e−0.05 + e−0.06 )) = 0.860719.
4 So, the answer is $860.72.
2. The current stock price is $90. According to your coworker, the time−1 price of this stock
will be uniformly distributed between $80 and $120. What is the expected rate of return
on this stock for this one year period and the model she is suggesting?
(a) About 12%.
(b) About 11.5%.
(c) About 11%.
(d) About 10.5%.
(e) None of the above.
Solution: (d)
The expected rate of return α satisﬁes
S (0)eα = E[S (1)] ⇒ α = ln 100
90 = ln(10/9) = 0.1053. 3. For a stock price that was initially $55.00, what is the price after 4 years if the continuously
compounded returns for these 4 years are 4.5%, 6.2%, 8.9%, and −3.2%?
(a) $59.08
(b) $64.80
(c) $74.80
(d) $84.10
(e) None of the above.
Solution: (b)
55e0.045+0.062+0.089−0.032 ≈ 64.80.
4. The current price of a continuousdividend paying stock is observed to be $50 per share
while its volatility is given to be 0.34. The dividend yield is projected to be 0.02.
The continuously compounded, riskfree interest rate is 0.05.
Consider a European call option with the strike price equal to $40 and the exercise date
in three months.
Using the BlackScholes pricing formula, ﬁnd the value VC (0) of this option at time−0.
(a) $9.08
(b) $9.80
(c) $10.55
(d) $14.10
(e) None...
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This note was uploaded on 08/04/2013 for the course M 339W taught by Professor Cudina during the Fall '12 term at University of Texas.
 Fall '12
 CUDINA
 Math

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