A three-month at-the-money call option on a stock index is trading at $5; the index is trading at $50. A forward start option on the index that comes to life in one month, has a life of three months from that point and that will be at-the-money when it comes to life, is trading at $4.98. The one-month rate of interest is 2% in continuously-compounded and annualized terms. What is the one-month forward price of the index?
A) $50.00
B) $50.05
C) $50.25
D) $50.45

Question

Quizplus · Accepted Answer

The one-month forward price of the index can be calculated using the formula for continuous compounding: $F = Se^{rt}$, where $S$ is the current spot price ($50), $r$ is the annualized interest rate (2% or 0.02), and $t$ is the time in years (1/12 for one month). Plugging in the values, we get $F = 50e^{0.02 \times (1/12)} \approx $50.05$.

A Three-Month At-The-Money Call Option on a Stock Index Is