1. This is about the current quoted futures price for a futures contract for delivery in 14 months of a bond paying, semi-annually, coupon at a rate of 5.2 percent per year on $100 face value, with a maturity of 11.45 years. The last coupon payment was 3 months ago. Assume that the term structure is flat with a rate of interest of 7% per year. Assume semi-annual compounding for valuation of bond and for determination of conversion factor. Assume continuous compounding for valuation of futures price. Use the information provided to find the following:
a) Conversion factor.
b) Cash spot price of bond.
c) Cash futures price.
d) Quoted futures price.
2. Use Black’s approximation to find the current fair values of a 13-month American call option with a strike price of 24 on a dividend paying stock trading at a current market price of 24, interest rate of 6.2 percent per year, continuously compounded and volatility of 0.32 (as a number, not percent). The stock will go ex-dividend every 3 months starting from time zero and the amount of each quarterly dividend is 4 percent of the current stock price. Obtain the following fair values of options needed to find Black’s approximate American call value:
a) European call option with maturity at first ex-dividend date.
b) European call option with maturity at second ex-dividend date.
c) European call option with maturity at third ex-dividend date.
d) European call option with maturity at fourth ex-dividend date.
e) European call option with maturity 13 months.
f) Current fair value of American call using Black’s approximation