4,459 research outputs found
A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options
We present a parallel algorithm for solving backward stochastic differential
equations (BSDEs in short) which are very useful theoretic tools to deal with
many financial problems ranging from option pricing option to risk management.
Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs
and non linear partial differential equations (PDEs in short) and hence enables
to solve high dimensional non linear PDEs. In this work, we apply it to the
pricing and hedging of American options in high dimensional local volatility
models, which remains very computationally demanding. We have tested our
algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear
speedups which proves the scalability of our implementationComment: 25 page
The INTERNODES method for the treatment of non-conforming multipatch geometries in Isogeometric Analysis
In this paper we apply the INTERNODES method to solve second order elliptic
problems discretized by Isogeometric Analysis methods on non-conforming
multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based
method that, on each interface of the configuration, exploits two independent
interpolation operators to enforce the continuity of the traces and of the
normal derivatives. INTERNODES supports non-conformity on NURBS spaces as well
as on geometries. We specify how to set up the interpolation matrices on
non-conforming interfaces, how to enforce the continuity of the normal
derivatives and we give special attention to implementation aspects. The
numerical results show that INTERNODES exhibits optimal convergence rate with
respect to the mesh size of the NURBS spaces an that it is robust with respect
to jumping coefficients.Comment: Accepted for publication in Computer Methods in Applied Mechanics and
Engineerin
A Parallel Algorithm for solving BSDEs - Application to the pricing and hedging of American options
We present a parallel algorithm for solving backward stochastic differential equations (BSDEs in short) which are very useful theoretic tools to deal with many financial problems ranging from option pricing option to risk management. Our algorithm based on Gobet and Labart (2010) exploits the link between BSDEs and non linear partial differential equations (PDEs in short) and hence enables to solve high dimensional non linear PDEs. In this work, we apply it to the pricing and hedging of American options in high dimensional local volatility models, which remains very computationally demanding. We have tested our algorithm up to dimension 10 on a cluster of 512 CPUs and we obtained linear speedups which proves the scalability of our implementationbackward stochastic differential equations, parallel computing, Monte- Carlo methods, non linear PDE, American options, local volatility model.
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