Efficient Long-dated Swaption Volatility Approximation in the Forward-LIBOR Model

We provide an efficient swaption volatility approximation in the lognormal forward-LIBOR model to accurately price for longer maturities and tenors. In particular, we approximate the swaption volatility with a mean update of... [ view full abstract ]

We provide an efficient swaption volatility approximation in the lognormal forward-LIBOR model to accurately price for longer maturities and tenors. In particular, we approximate the swaption volatility with a mean update of the spanning forward rates. Since the joint distribution of the spanning forward rates is not known we resort to numerical discretisation techniques. More specifically, we approximate the mean forward rates with a multi-dimensional weak order 2.0 Itō-Taylor scheme. We test our approximation with a quasi-Monte Carlo study and find it to be substantially more effective when compared to existing approximations for longer maturities and tenors.