Final answer:
The long position payoff at expiration for a call option on an interest rate with the terms given will be $0, as the market rate at expiration (6.53%) is below the exercise rate (8%), meaning there would be no incentive for the option holder to exercise this option.
Step-by-step explanation:
To calculate the long position payoff at expiration for a call option on an interest rate where the underlying is a 180-day interest rate at 6.53 percent at expiration, the notional principal is $10 million, and the exercise rate is 8%, we need to understand the concept of the call option on interest rates.
A call option on an interest rate gives the holder the right to benefit from a rise in interest rates above a specified rate (exercise rate or strike rate). Since the exercise rate is 8% and the underlying rate at expiration is 6.53%, which is below the strike rate, the call option will not be exercised, as it would not be profitable to do so. Therefore, the long position payoff at expiration would be $0 because the holder of the option would not exercise their right to 'buy' the interest at 8% when the market rate is 6.53%.
In this case, the notional principal amount does not directly play into the calculation for the payoff because no actual exchange of principal occurs when dealing with interest rate options; the notional amount is simply used to calculate the gains or losses should the option be exercised, which it will not be in this scenario.