104 research outputs found
Pricing path-dependent Bermudan options using Wiener chaos expansion: an embarrassingly parallel approach
In this work, we propose a new policy iteration algorithm for pricing
Bermudan options when the payoff process cannot be written as a function of a
lifted Markov process. Our approach is based on a modification of the
well-known Longstaff Schwartz algorithm, in which we basically replace the
standard least square regression by a Wiener chaos expansion. Not only does it
allow us to deal with a non Markovian setting, but it also breaks the
bottleneck induced by the least square regression as the coefficients of the
chaos expansion are given by scalar products on the L^2 space and can therefore
be approximated by independent Monte Carlo computations. This key feature
enables us to provide an embarrassingly parallel algorithm.Comment: The Journal of Computational Finance, Incisive Media, In pres
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
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.
Asymptotic normality of randomly truncated stochastic algorithms
International audienceWe study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice
Long time behaviour of a stochastic nano particle
In this article, we are interested in the behaviour of a single ferromagnetic
mono-domain particle submitted to an external field with a stochastic
perturbation. This model is the first step toward the mathematical
understanding of thermal effects on a ferromagnet. In a first part, we present
the stochastic model and prove that the associated stochastic differential
equation is well defined. The second part is dedicated to the study of the long
time behaviour of the magnetic moment and in the third part we prove that the
stochastic perturbation induces a non reversibility phenomenon. Last, we
illustrate these results through numerical simulations of our stochastic model.
The main results presented in this article are the rate of convergence of the
magnetization toward the unique stable equilibrium of the deterministic model.
The second result is a sharp estimate of the hysteresis phenomenon induced by
the stochastic perturbation (remember that with no perturbation, the magnetic
moment remains constant)
Stein estimation of the intensity of a spatial homogeneous Poisson point process
In this paper, we revisit the original ideas of Stein and propose an
estimator of the intensity parameter of a homogeneous Poisson point process
defined in and observed in a bounded window. The procedure is based on a
new general integration by parts formula for Poisson point processes. We show
that our Stein estimator outperforms the maximum likelihood estimator in terms
of mean squared error. In particular, we show that in many practical situations
we have a gain larger than 30\%
Pricing Parisian options using Laplace transforms
International audienceIn this work, we propose to price Parisian options using Laplace transforms. Not only do we compute the Laplace transforms of all the different Parisian options, but we also explain how to invert them numerically. We prove the accuracy of the numerical inversion
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