1. Market rates are currently 5%. A $1,000 par corporate bond carries a coupon rate of 6%, pays coupons semiannually, and has ten coupon payments remaining to maturity. There are 90 days between settlement and the next coupon payment. Which of the following is closest to the dirty and clean prices of the bond？
A. $1,043.76, $1,013.76
B. $1,043.76, $1,028.76
C. $1,056.73, $1,041.73
D. $1,069.70, $1,054.70
The dirty price of the bond 90 days ago is calculated as N = 10; I/Y = 2.5; PMT = 30; FV = 1,000; CPT→PV = 1,043.76. Adjusting the PV for the fact that there are only 90 days until the receipt of the first coupon, then the dirty price now is
2、1. How to create a bull spread ？
A. Buy a put with a strike price of X= 55, and sell a put with a strike price of 50.
B. Buy a put with a strike price of X = 50, and sell a put with a strike price of 55.
C. Buy a call with a premium of 5, and sell a call with a premium of 7
D. Buy a call with a strike price of X = 50, and sell a put with a strike price of 55.
A bull spread involves buying a put with a low strike price and selling another put with a high strike price or buying a call with a low strike price and selling another call with a high strike price.
3、 The risk-free rate is 10%.Assume that options on a non-dividend paying stock with price of USD 100 have a time to expiry of half a year and a strike price of USD 110. Further, , the Black-Scholes values of these option Is closest to：
A. Value of American call option is USD 6.56 and of American put option is USD 12.0
B. Value of American call option is USD 5.50 and of American put option is USD 12.0
C. Value of American call option is USD 6.56 and of American put option is USD 10.0
D. Value of American call option is USD 5.50 and of American put option is USD 10.0
We know that American options are never less than corresponding European option in valuation. Also, the American call option price is exactly the same as the European call option price under the usual Black-Scholes world with no dividend. Thus only ‘a’ is the correct option.
4、There is a two-year bond that pays an annual coupon of 10% and whose current yield to maturity is 14%，what are the duration and convexity? Use $1,000 as the face value.
A. 1.637 years and 3.3491
B. 1.732 years and 4.0283
C. 1.892 years and 4.2276
D. 1.906 years and 4.3278
The duration is 1.906 years, as shown in the table. Therefore the correct answer has to be D; you don';t need to compute the convexity.