Related papers: Pricing approximations and error estimates for loc…
To model subsurface flow in uncertain heterogeneous\ fractured media an elliptic equation with a discontinuous stochastic diffusion coefficient - also called random field - may be used. In case of a one-dimensional parameter space, L\'evy…
We establish an explicit pricing formula for the class of L\'evy-stable models with maximal negative asymmetry (Log-L\'evy model with finite moments and stability parameter $1<\alpha\leq 2$) in the form of rapidly converging series. The…
In a high-frequency context, we investigate the efficient estimation of scaling and jump activity parameters for a stochastic differential equation driven by a L{\'e}vy process with both diffusion component and pure-jump component. We first…
We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the…
Given a multi-dimensional It\^{o} process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the It\^{o} process at each fixed time.…
Based on the concept of self-decomposability, we extend some recent multivariate L\'evy models built using multivariate subordination with the aim of capturing situations in which a sudden event in one market is propagated onto related…
Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be…
The L\'evy-stable distribution is the attractor of distributions which hold power laws with infinite variance. This distribution has been used in a variety of research areas, for example in economics it is used to model financial market…
The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…
We analyze the valuation partial differential equation for European contingent claims in a general framework of stochastic volatility models where the diffusion coefficients may grow faster than linearly and degenerate on the boundaries of…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
We present an overview of the broad class of financial models in which the prices of assets are L\'evy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
Model approximations are common practice when estimating structural or quasi-structural models. The paper considers the econometric properties of estimators that utilize projections to reimpose information about the exact model in the form…
We derive globally reliable a posteriori error estimators for a PDE-constrained optimization problem involving linear models in fluid dynamics as state equation; control constraints are also considered. The corresponding local error…
Observing prices of European put and call options, we calibrate exponential L\'evy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for L\'evy models of finite jump activity as well as…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
This paper is a supplement to our recent paper ``Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in L\'evy models". We introduce the class of regime-switching L\'evy models with memory,…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
The accuracy of least squares calibration using option premiums and particle filtering of price data to find model parameters is determined. Derivative models using exponential L\'evy processes are calibrated using regularized weighted…