We develop policy gradients methods for stochastic control with exit time in a model-free setting. We propose two types of algorithms for learning either directly the optimal policy or by learning alternately the value function (critic) and the optimal control (actor). The use of randomized...

In this short note, we consider the issue of negative intensities when using an Hull-White model. We show how to solve this drawback by slightly modifying the zero-coupon analytical formula available for Gaussian models

In this short note, we derive a new approximation for the pricing of Vanillas in the case of a Black-Scholes model with affine dividends. This new approximation is more accurate than the Bos-al formula [Bos], commonly used by practitioners

The so-called distribution mapping is a technique, commonly used by practitioners in fixed-income, that allows to tweak model 1D-dis\-tri\-bu\-tions into market $1$D-distributions. This technique is intended to overcome the shortcomings of standard fixed-income diffusion models which do not...

Starting with three classical examples in financial mathematics, mainly the calibration of n-dimensional Hull-White covariance matrices on at-the-money swaptions/CMS spread options and the construction of correlation matrices with fixed subcorrelations for multi-factor stochastic volatility...

We present an efficient algorithm for computing the Vega KT in the local volatility model based on the calculation of the local Vega through Monte-Carlo simulation and algorithmic differentiation. In comparison with the PDE algorithm presented in [Guennoun], our algorithm is applicable for...

In this paper, we present a local volatility model with stochastic dividends. The dividends, for which we provide a simple parametrization, are modeled as a function of the underlying. The calibration of the local volatility on market Vanillas is then achieved using a PDE algorithm. We...

We obtain some new (Malliavin) probabilistic representations for the so-called break-even in Local Volatility (LV) and Local Stochastic Volatility (LSV) models for which we get some approximations extending the formulas derived in [Bergomi] in the ATM case. These break-even correspond to the...

Following our papers \cite{HL13,Nat22} on the computation of the Vega $KT$ under the local volatility model, we consider local stochastic volatility models in the present article. Our algorithm is based on the calculation of the local Vega through Monte-Carlo simulation and algorithmic...

The local volatility model is widely used as this is the unique one-factor Markov model perfectly calibrated to a continuum of vanilla options in strike and expiry. It requires unfortunately an arbitrage-free interpolation of implied volatility in expiry and a time-consuming Euler discretization...