Question

Suppose that the 3-year risk-free interest rate is 4% with continuous compounding. You are a bank offering a client a principal-protected note. The 3-year risk-free bond is on a principal (face/par value) of $1,000. The client has $1,000 to invest You plan to use a 3-year call option on a stock portfolio worth $1,000 that does not pay any dividends. The portfolio volatility is 30%

a) What is the price of the risk-free bond today?
b) How much is the difference between the face value of $1,000 and the price of the bond?
c) Use the option pricing calculator to determine the call option price if the exercise price is 1,000
d) Do you have enough to buy the option if its exercise price is 1,000?

Answer 1

a) The price of the risk-free bond today is $916.50.

b) The difference between the face value and the bond price is $83.50.

c) The call option price is $66.19, and the client has enough funds to purchase it with a $1,000 initial investment.

Step-by-step explanation:

a) The price of the risk-free bond today is $916.50, calculated using the continuous compounding formula, considering the 4% risk-free interest rate over a 3-year period. This represents the present value of the future face value. b) The difference between the face value and the bond price is $83.50. This difference is essentially the cost or investment required by the client. In this scenario, it's the amount the client needs to invest initially to participate in the principal-protected note.

c) The call option price is determined using the Black-Scholes model, incorporating factors such as stock price, exercise price, time to maturity, risk-free rate, and volatility. With an exercise price of $1,000, the calculated call option price is $66.19. This option provides the client with the right, but not the obligation, to buy the stock portfolio at the predetermined exercise price.

d) The client does have enough funds to buy the option, as the cost of the option is $66.19, which is less than the initial investment amount of $83.50. This leaves the client with sufficient funds after purchasing the option. In summary, the client can invest in the principal-protected note by purchasing the risk-free bond and a call option, utilizing their available funds effectively.