w_exam_one_solutions

1 consider the following binomial interest rate tree

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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 interest-rate tree modeling the future evolution of annual continuously compounded interest rates. The period-length is one year. 0.06 0.055 0.05 0.05 0.045 0.04 The risk-neutral probability is given to be equal to 1/2. What is the price of a zero-coupon 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 one-dollar, zero-coupon 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 continuous-dividend 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, risk-free 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 Black-Scholes 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.

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