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...

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...

We revisit the classical Merton's optimal allocation problem and show that significant corrections to the Merton ratio arise from hard to observe behaviour of the volatility process around zero. Having regularised this behaviour, we show that the adjustment to the myopic Merton ratio can be...

Financial derivatives linked to the median, which is the 50%-th percentile of a distribution, have not been extensively studied in realistic models of financial markets, as such derivatives simply did not exist until recently. The Libor reform that brought a seismic change to the interest rate...