When the interest rate is 5% per annum with continuous compounding, which of the following creates a $1000 principal protected note?
A) A one-year zero-coupon bond plus a one-year call option worth about $59
B) A one-year zero-coupon bond plus a one-year call option worth about $49
C) A one-year zero-coupon bond plus a one-year call option worth about $39
D) A one-year zero-coupon bond plus a one-year call option worth about $29

Question

Quizplus · Accepted Answer

To create a principal protected note, we need to buy a zero-coupon bond and a call option. The strike price of the call option should be equal to the face value of the zero-coupon bond. The cost of the call option should be such that the total cost of the bond and the option is equal to the principal amount. Let P be the principal amount, r be the interest rate, and t be the time period. Then the cost of the zero-coupon bond is P*e^(-rt), and the cost of the call option is P - P*e^(-rt), which simplifies to P*(1 - e^(-rt)). Substituting r = 5% and t = 1 year, we get the cost of the bond as 1000*e^(-0.05*1) = 951.23, and the cost of the option as 1000*(1 - e^(-0.05*1)) = 48.77. The closest option to this value is B, with a cost of about $49.

When the Interest Rate Is 5% Per Annum with Continuous