Derivatives credit risk under Basel I

Does an interest rate swap with a negative value increase the credit risk of a financial institution? 

Yes. If the value of the swap becomes positive during its lifetime, and the counter-party defaults, it constitutes a loss.

How is the capital requirement calculated under Basel 1?

Under Basel 1, the add-on factor for interest rate derivatives with a maturity under five years is 0.5% of the principal.