We relate the Lp-variation, 2≤p∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in...

For a stopped diffusion process in a multidimensional time-dependent domain , we propose and analyse a new procedure consisting in simulating the process with an Euler scheme with step size [Delta] and stopping it at discrete times in a modified domain, whose boundary has been appropriately...

We study the -time regularity of the Z-component of a Markovian BSDE, whose terminal condition is a function g of a forward SDE (Xt)0=t=T. When g is Lipschitz continuous, Zhang (2004) [18] proved that the related squared -time regularity is of order one with respect to the size of the time mesh....

We study the error induced by the time discretization of decoupled forward-backward stochastic differential equations (X,Y,Z). The forward component X is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XN with N time steps. The backward component...

This short note corrects an error (a factor is missing) in two formulas related to L <Superscript>2</Superscript>-limits, established in “Discrete time hedging errors for options with irregular payoffs” by E. Gobet and E. Temam, Finance and Stochastics, 5, 357–367 (<CitationRef CitationID="CR6">2001</CitationRef>). Copyright Springer-Verlag Berlin Heidelberg...</citationref></superscript>

Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of the payoff function. Our approach relies on an...

In this article we present a continuous time model for natural gas and crude oil future prices. Its main feature is the possibility to link both energies in the long term and in the short term. For each energy, the future returns are represented as the sum of volatility functions driven by...

This overview article concerns the notion of fractional smoothness of random variables of the form $g(X_T)$, where $X=(X_t)_{t\in [0,T]}$ is a certain diffusion process. We review the connection to the real interpolation theory, give examples and applications of this concept. The applications in...

We are interested in approximating a multidimensional hypoelliptic diffusion process (Xt)t[greater-or-equal, slanted]0 killed when it leaves a smooth domain D. When a discrete Euler scheme with time step h is used, we prove under a noncharacteristic boundary condition that the weak error is...