There are numerous models for specifying the uncertainty of future instantaneous volatility or variance, including the Heston, SABR and ZABR models. Often it is observed that a specific stochastic volatility model is chosen not for particular dynamical features, relevant for exotic payoff...

"The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity...

This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is...

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...