The Black-Scholes-Merton model assumes (circle one)
The return from the stock in a short period of time is lognormal
The stock price at a future time is lognormal
The stock price at a future time is normal
None of the above
11. Volatility can be defined as (circle one)
The standard deviation of the return, measured with continuous compounding, in one year
The variance of the return, measured with continuous compounding, in one year
The standard deviation of the stock price in one year
12. A stock price is $100. Volatility is estimated to be 20% per year. What is the an estimate of the standard deviation of the change in the stock price in one week (circle one)
$0.38
$2.77
$3.02
$0.76
13. To create a range forward contract in order to hedge foreign currency that will be paid a company should (Circle one)
Buy a put and sell a call on the currency with the strike price of the put higher than that of the call
Buy a put and sell a call on the currency with the strike price of the put lower than that of the call
Buy a call and sell a put on the currency with the strike price of the put higher than that of the call
Buy a call and sell a put on the currency with the strike price of the put lower than that of the call
14. Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $1,000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.
a. What was the price of this bond when it was issued? $1,000.
b. Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment?1000.
c. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment? $930.
15. What is the price of a five-year, zero-coupon, default-free security of 4.8% with a face value of $1,000? $48.
16. Draw the diagram that tells you if you buy a Bond what its relationship is to Call Yield, Yield to Maturity, and Yield to...
A bond can be "recalled" at its maturity date if the percentage rate has gone down because it can be refinanced at a lower cost, if the percentage rate has gone up, you would do nothing because it is now a better deal. Yield to Maturity is the rate of return expected if the bond is held until maturity. Yield to a Call is when you redeem the bond at the callable date, which is before maturity.
17. Using a binomial tree, what is the price of a $40 strike 6-month call option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, ? = 0.35
2.50
2.76
2.92
3.08
18. Compute ? For the following call option. The stock is selling for $23.50. The strike price is $25. The possible stock prices at the end of 6 months are $27.25 and $21.75.
A) 0.4091
B) 0.6822
C) 0.8433
D) 0.9216
19. Using a binomial tree, what is the price of a $40 strike 6-month put option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, ? = 0.35
A) $3.52
B) $3.66
C) $3.84
D) $3.91
20. What is the delta on a $25 strike put? Assume S = $24.00, ? = 0.35, r = 0.06, the stock pays a 2.0% continuous dividend and the option expires in 40 days?
A) 0.582
B) 0.602
C) 0.662
D) 0.702 although when I put this data into a calculator online, I came up with 0.9984 as the answer.
21. Assume S = $33.00, ? = 0.32, r = 0.06, div = 0.01. You short 100 $35 strike calls at 68 days until expiration. Under a delta hedge position, what is your overnight profit/loss if the stock rises to $34.50?
A) $9.23 loss
B) $9.23 gain
C) $7.62 loss
D) $7.62 gain
22. A European call option on a certain stock has a strike price of $30, a time to maturity of one year and an implied volatility of 30%. A put option on the same stock has a strike price of $30, a time to maturity of one year and an implied volatility of 33%. What is the arbitrage opportunity open to a trader. Does the opportunity work only when the lognormal assumption underlying Black-Scholes holds. Explain…
