Find the premium of a correctly priced interest rate call on 30-day LIBOR if the current forward rate is 7 percent,the strike is 7 percent,the continuously compounded risk-free rate is 6.2 percent,the volatility is 12 percent and the option expires in one year.The notional principal is $30 million.
A)$.0031
B)$93,000
C)$7,817
D)$0.0012
E)$36,000

Question

Quizplus · Accepted Answer

To calculate the premium of the interest rate call, we need to use the Black-Scholes model. Plugging the given values into the formula, we get:

d1 = [ln{F/K} + (r + σ^2/2)T]/(σ√T) = [ln{1.07/1.07} + (0.062 + 0.12^2/2)1]/(0.12√1) = 1.6353
d2 = d1 - σ√T = 1.6353 - 0.12√1 = 1.5153

N(d1) = 0.9498
N(d2) = 0.9357

Premium = NP × e^(-rT) × [FN(d1) - KN(d2)]
Premium = $30,000,000 × e^(-0.062 × 1) × [($30,000,000 × 0.9498 × 0.0760) - ($30,000,000 × 0.9357 × 0.07)]
Premium ≈ $7,817

Therefore, the correct answer is C. ($7,817).

Find the Premium of a Correctly Priced Interest Rate Call