Fair Value of the Bond Forward Contract
Not quite.
The difference is discounted over the remaining contract period.
Suppose that nine months ago, you purchased a USD bond contract with twelve months to expiration, on a notional value of USD 5,500,000 for USD 100 (as a percentage of par). Six months later, the current forward price was USD 115 (as a percentage of par), and the annualized six-month risk-free rate was 0.75%.
The value of the USD-bond forward position was closest to:
You got it!
Since both prices are given as percentages, it's simply the present value of the difference in price times the notional amount.
$$\displaystyle V_t = PV[F_t - F_0]$$
So,
$$\displaystyle \frac{(115 - 100)}{(1+0.0075)^{\frac{6}{12}}} = 14.9441$$.
Note that the values are given as a percentage of par, so the result will also be a percentage.
Then,
$$\displaystyle 0.149441 \times 5{,}500{,}000 = 821{,}925.5$$.
No.
The discount period is the time remaining in the contract.
USD 821,926.
USD 823,460.
USD 825,000.
