In this paper we consider the optimal stopping problem for general dynamic monetary utility functionals. Sufficient conditions for the Bellman principle and the existence of optimal stopping times are provided. Particular attention is payed to representations which allow for a numerical...

This paper applies to the static hedge of barrier options a technique, mean-square hedging, designed to minimize the size of the hedging error when perfect replication is not possible. It introduces an extension of this technique which preserves the computational efficiency of mean-square...

Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of...

The Heston model stands out from the class of stochastic volatility (SV) models mainly for two reasons. Firstly, the process for the volatility is nonnegative and mean-reverting, which is what we observe in the markets. Secondly, there exists a fast and easily implemented semi-analytical...

Barrier options under wide classes of L\'evy processes with exponential jump densities, including Variance Gamma model, KoBoL (a.k.a. CGMY) model and Normal Inverse Gaussian processes, are studied. The leading term of asymptotics of the option price and the leading term of asymptotics in Carr's...

Gram-Charlier expansions have became popular in Finance as an improvement over the normality assumption. The reason is that in Gram-Charlier expansions, parameters appear which directly control the skewness and kurtosis. Those expansions, of polynomial nature, have the unfortunate drawback of...

We present a method for simulating yield curve dynamics by learning the curve distribution from historical data using Artificial Neural Networks (ANN) in a two step procedure. The first step involves an autoencoder which performs a quantization of curve moves, generating a set of representative...

The "SSVI" (aka "S3") implied volatility curve is the simplest curve that has three parameters to describe the at-the-money behavior of implied volatilities for a given term, while also having a sensible functional form in the call and put wings. We describe the necessary and sufficient...