This paper describes a new parametric volatility surface that is arbitrage free, extremely rich and flexible, and has closed-form expressions for both European option values and local volatilities. Our surface is based on the work of Carr and Pelts, for which we provide a simple derivation and a...

Stochastic volatility models are widely used in interest rate modeling to match the option smiles -- the two most popular are the Heston model and the SABR one. These have been incorporated into arbitrage-free term structure frameworks, Heston-LMM and SABR-LMM respectively.In this paper we...

In the current low-interest-rate environment, extending option models to negative rates has become an important issue. In our previous paper, we introduced the Free SABR model, which is a natural and an attractive extension to the classical SABR model. In spite of its advantages over the Shifted...

Artificial Neural Networks (ANNs) have recently been proposed as accurate and fast approximators in various derivatives pricing applications. ANNs typically excel in fitting functions they approximate at the input parameters they are trained on, and often are quite good in interpolating between...

We generalize the algorithmic differentiation method proposed by Antonov (2016) from price Greeks to XVA Greeks. This method, named Backward Differentiation (BD), was developed in the context of computing price or PV Greeks for individual callable exotic trades.We start by treating cases where...

In this paper, we present advanced analytical formulas for SABR model option pricing. The first technical result consists of a new exact formula for the zero correlation case. This closed form is a simple 2D integration of elementary functions, particularly attractive for numerical...

In this article, we present the analytical approximation of zero-coupon bonds and swaption prices for general short rate models. The approximation is based on regular and singular expansions with respect to the small volatility and contains a low-dimensional integration. The model in hand...

The modeling of tenor basis spreads is of central importance to CVA for tenor basis swaps. Such spreads are typically positive, suggesting a natural lower bound. We introduce a multi- curve Cheyette-style model with lower bounds enforced through level dependence in spread volatilities. The model...

This paper presents a discrete framework on event time grid, for a cross-currency term structure modelling. The discrete model is generic, in the sense that it can link together any single currency model to form a multi-factor cross currency model, provided that it is known (analytically or...