If the (1,1.5)-year forward rate is lognormal with volatility $\sigma = 0.15$ ,and the one-year spot rate is 4%,what is the NPV of a $100,000-notional $12 \times 18$ -FRA at a 5% strike rate if the (1,1.5)-year forward rate is 6%,as seen from the buyer's point of view? (Assume the Black model applies for interest-rate options. )
A) $- \$ 470.88$
B)$0
C)$475.61
D)$480.39

Question

Quizplus · Accepted Answer

The NPV of a FRA from the buyer's perspective can be calculated using the Black model for interest-rate options. Given the parameters, the calculation involves determining the present value of the expected payoff from the FRA, considering the difference between the forward rate and the strike rate, adjusted for the probability of the payoff occurring (using the Black model's d1 and d2), and discounted back at the forward rate. The positive NPV indicates the buyer would have a gain from entering into the FRA, given the specified conditions.

If the (1,1 σ=0.15\sigma = 0.15σ=0.15 ,And the One-Year Spot Rate Is 4%,what Is the NPV

If the (1,1 $\sigma = 0.15$ ,And the One-Year Spot Rate Is 4%,what Is the NPV