Two Curves Upfront

At the end of last year Peter Caspers released a short paper Normal Libor in Arrears. I could not help but wonder if this was not the result of the update to a library which had previously used Black’s model for the convexity correction. In the summer of 2011, like many others, I had to very quickly update an interest rate pricing library to allow for negative interest rates when CHF became negative. It was a little bizarre, the ability to admit negative rates was often seen as a weakness in interest rate models, such as shifted lognormal or bpvol, yet suddenly it became their strength. This point was discussed further in the Risk magazine article, Negative Rates: Dealers struggle to price 0% floors.

To help with practical implementation, I re-derived the results, explicitly allowing for two curve pricing and freeing up the payment date from the LIBOR start date which can be useful for various date adjustments and indeed range accruals.

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