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Pricing high-dimensional Bermudan options with hierarchical tensor formats.
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TLDR
In this paper, an efficient compression technique based on hierarchical tensors for popular option pricing methods is presented, which can be used for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method, both using high-dimensional tensorized polynomial expansions.Abstract:
An efficient compression technique based on hierarchical tensors for popular option pricing methods is presented. It is shown that the "curse of dimensionality" can be alleviated for the computation of Bermudan option prices with the Monte Carlo least-squares approach as well as the dual martingale method, both using high-dimensional tensorized polynomial expansions. This discretization allows for a simple and computationally cheap evaluation of conditional expectations. Complexity estimates are provided as well as a description of the optimization procedures in the tensor train format. Numerical experiments illustrate the favourable accuracy of the proposed methods. The dynamical programming method yields results comparable to recent Neural Network based methods.read more
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References
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TL;DR: This paper presents a meta-modelling procedure that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually computing random numbers and random Variables.
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Valuing American Options by Simulation: A Simple Least-Squares Approach
TL;DR: In this paper, a new approach for approximating the value of American options by simulation is presented, using least squares to estimate the conditional expected payoff to the optionholder from continuation.
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Tensor-Train Decomposition
TL;DR: The new form gives a clear and convenient way to implement all basic operations efficiently, and the efficiency is demonstrated by the computation of the smallest eigenvalue of a 19-dimensional operator.
Journal ArticleDOI
Efficient classical simulation of slightly entangled quantum computations.
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