Pricing of interest rate derivatives, such as CMS spread or mid-curve options, depends on modelling the underlying single rates. For flexibility and realism, these rates are often described in the framework of stochastic volatility models. In this paper, we allow rates to be modelled within a...

We provide an efficient swaption volatility approximation for longer maturities and tenors, under the lognormal forward-LIBOR model. In particular, we approximate the swaption volatility with a mean update of the spanning forward rates. Since the joint distribution of the forward rates is not...

We present an algorithm to approximate moments for forward rates under a displaced lognormal forward-LIBOR model (DLFM). Since the joint distribution of rates is unknown, we use a multi-dimensional full weak order 2.0 Ito-Taylor expansion in combination with a second-order Delta method. This...