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...

After Lehman default (credit crisis 2007), practitioners considered the default risk as a major risk. The regulators pushed the industry to use collateral in order to reduce the risk. In this new world, we want to see how this new considerations affect the theory related to the Partial...

We propose an approach for the dynamical estimation of initial margins. We determine initial margins at future points in time by computing a risk measure of the modelled price increment over a margin period of risk. As an example, we produce the initial margin process for interest rate swap...

We analyze corporate financial policies in leveraged buyouts (LBOs) in the presence of default risk. Our model captures the LBO-specific stepwise debt reduction, either with predetermined or cash-flow dependent (cash sweep) principal payments, and thus allows for dynamic redemption. These...

We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is...