Question

For a $1.50/£ call option with an initial premium of $0.033/£ and a rho value of 0.2, after an increase in the U.S. dollar rate from 8% to 9% - the new ATM option premium would be:

A) $0.037/£.
B) $1.55/£
C) $0.036/£.
D) $0.035/£

Answer 1

To calculate the new ATM option premium after an increase in the U.S. dollar rate, we use the ρ value to determine the change in the option premium. The change in premium is 0.2% of the initial premium, and adding this change to the initial premium gives us the new ATM option premium of $0.033066/£.

To calculate the new ATM option premium, we first need to calculate the change in the option premium caused by the change in the U.S. dollar rate. The ρ value represents the change in option premium for a 1% change in the underlying currency rate.

Since the ρ value is 0.2, a 1% increase in the U.S. dollar rate will cause a 0.2% increase in the option premium. The initial premium is $0.033/£, so the change in premium is 0.2% of $0.033/£.

Change in premium = 0.2% of $0.033/£ = $0.000066/£

Thus, the new ATM option premium would be:

Initial premium + Change in premium = $0.033/£ + $0.000066/£ = $0.033066/£