Valuation and Risk Management of Vanilla LIBOR Swaptions in a Fallback

Regulators and central banks are defining-through mathematical formulae-the market microstructure for the calculation of fixings for LIBOR interest rate swaps in terms of the relevant swap rates that reference the Risk-Free Rate that will replace a particular LIBOR post its cessation. The nonlinear mappings proposed from the swap rate that references the Risk-Free Rate index to the LIBOR swap rate that can be used contractually to value derivative instruments, such as vanilla European swaptions, introduce convexity effects. We use the market standard SABR model for vanilla European interest rate options to derive a valuation formula for a swaption whose payoff involves a LIBOR swap rate constructed from a nonlinear function of a swap rate on a Risk-Free Rate index. Our analysis shows that the convexity effects can be expressed as symmetric quadratic derivatives, which we value analytically with the SABR model. The methodology we develop is analytic, based entirely on the SABR model, satisfies call-put parity for LIBOR swaptions, requires no opaque parameters, and has risk factors that can be projected onto liquid market instruments