Problem 5

Today is period 0, and the length between the periods is one year. In the fixed-income securities market you observe the following four securities.

Security A: It is a four-year regular coupon bond with an annual coupon payments of $100.00 and a face value of $1,000.00. The next coupon payment is one year from now. Security A can be bought or issued at a price of $945.3667 per bond.

Security B: It is a forward contract. The contract matures on period 1, and the forward price is $1,409.3762. The security underlying the forward contract matures on period 4 with a face value of $2,000.00. You may go short (sell) or long (buy) on this contract.

Security C: It is an annuity. It pays $1.00 on periods 1, 2, 3, and 4. It can be bought or issued at a price of $3.0774 per one annuity.

Security D: It is a zero-coupon bond. It matures in period 1, and it has a face value of $1,000.00. It can be bought or issued at a price of $X per unit.

As per the no-arbitrage principle, what is the current theoretical value of Security D? In other words, what is the value X?

(Round-off to at least four decimal places.)