Search results for "Backward"

Backward Frequency Doubling in Periodically Poled Lithium Niobate in the Pulsed Regime

2011

On the Pricing and Hedging of Options on Commodity Forward and Futures Contracts - A Note

2007

In recent years there appeared some organized markets for forward contracts and options on these contracts. In this paper we review shortly the organization of trade on a centralized forward market. Assuming a friction-free market with constant interest rate we build a consistent continuous time framework for the valuation and hedging of options on a forward or a futures contract. This framework takes into account the peculiarities of a forward/futures contract. In our framework we consider the pricing and hedging of options on a forward contract and reconsider the Black-76 model for the pricing and hedging of options on a futures contract.

$L_2$-variation of L\'{e}vy driven BSDEs with non-smooth terminal conditions

2016

We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\'{e}vy process $(X_t)_{t\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the L\'{e}vy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.

Mean square rate of convergence for random walk approximation of forward-backward SDEs

2020

AbstractLet (Y,Z) denote the solution to a forward-backward stochastic differential equation (FBSDE). If one constructs a random walk$B^n$from the underlying Brownian motionBby Skorokhod embedding, one can show$L_2$-convergence of the corresponding solutions$(Y^n,Z^n)$to$(Y, Z).$We estimate the rate of convergence based on smoothness properties, especially for a terminal condition function in$C^{2,\alpha}$. The proof relies on an approximative representation of$Z^n$and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the partial differential equation associated to the FBSDE, as well as of the finite difference equations associated to t…

Simulation of BSDEs with jumps by Wiener Chaos Expansion

2016

International audience; We present an algorithm to solve BSDEs with jumps based on Wiener Chaos Expansion and Picard's iterations. This paper extends the results given in Briand-Labart (2014) to the case of BSDEs with jumps. We get a forward scheme where the conditional expectations are easily computed thanks to chaos decomposition formulas. Concerning the error, we derive explicit bounds with respect to the number of chaos, the discretization time step and the number of Monte Carlo simulations. We also present numerical experiments. We obtain very encouraging results in terms of speed and accuracy.

Donsker-Type Theorem for BSDEs: Rate of Convergence

2019

In this paper, we study in the Markovian case the rate of convergence in Wasserstein distance when the solution to a BSDE is approximated by a solution to a BSDE driven by a scaled random walk as introduced in Briand, Delyon and Mémin (Electron. Commun. Probab. 6 (2001) Art. ID 1). This is related to the approximation of solutions to semilinear second order parabolic PDEs by solutions to their associated finite difference schemes and the speed of convergence. peerReviewed

Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition

2018

In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the L2-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution u of the associated PDE. Here we improve existing results by showing some properties of the second derivative of u in space. peerReviewed

A Multivariate Non-Gaussian Stochastic Volatility Model with Leverage for Energy Markets

2009

Spot prices in energy markets exhibit special features like price spikes, mean-reversion inverse, stochastic volatility, inverse leverage effect and co-integration between the different commodities. In this paper a multivariate stochastic volatility model is introduced which captures these features. Second order structure and stationary issues of the model are analysed. Moreover the implied multivariate forward model is derived. Due to the flexibility of the model stylized facts of the forward curve as contango, backwardation and humps are explained. Moreover, a transformed-based method to price options on the forward is described, where fast and precise algorithms for price computations ca…

Pricing of Forwards and Options in a Multivariate Non-Gaussian Stochastic Volatility Model for Energy Markets

2013

In Benth and Vos (2013) we introduced a multivariate spot price model with stochastic volatility for energy markets which captures characteristic features, such as price spikes, mean reversion, stochastic volatility, and inverse leverage effect as well as dependencies between commodities. In this paper we derive the forward price dynamics based on our multivariate spot price model, providing a very flexible structure for the forward curves, including contango, backwardation, and hump shape. Moreover, a Fourier transform-based method to price options on the forward is described.

Precision electroweak measurements on the Z resonance

2005

We report on the final electroweak measurements performed with data taken at the Z resonance by the experiments operating at the electron-positron colliders SLC and LEP. The data consist of 17 million Z decays accumulated by the ALEPH, DELPHI, L3 and OPAL experiments at LEP, and 600 thousand Z decays by the SLD experiment using a polarised beam at SLC. The measurements include cross-sections, forward-backward asymmetries and polarised asymmetries. The mass and width of the Z boson, $\MZ$ and $\GZ$, and its couplings to fermions, for example the $\rho$ parameter and the effective electroweak mixing angle, are precisely measured. The number of light neutrino species is determined to be 2.9840…