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

Today is period 0, and the length between the periods is one year. In the fixed-income securities market you observe following three securities. An investor can buy or sell fraction of a fixed-income security.

Security A: It is a zero-coupon bond. It matures in period 1, and it has a face value of $100. It can be bought or issued at a current price of $X.

Security B: It is a zero-coupon bond. It matures in period 2, and it has a face value of $1,000. It can be bought or issued at a current price of $876.870.

Security C: It is a forward contract. The contract matures on period 1, and the forward price is $92.312. The security underlying the forward contract matures on period 2 with a face value of $100. You may go short (sell) or long (buy) on this contract. (Hint: At t=0 if you buy a forward contract, then you will pay $92.312 at the end of year 1 (t=1), and then you will receive $100 at the end of year 2 (t=2).)

As per the no-arbitrage principle, what should be the theoretical (fundamental) value of Security A, i.e., what is X?

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