Pricing Bermudan Options via Multilevel Approximation Methods
TLDR
A novel approach to reducing the computational complexity of various approximation methods for pricing discrete time American or Bermudan options by proposing a multilevel low biased estimate for the price of the option.Abstract:
In this article we propose a novel approach to reducing the computational complexity of various approximation methods for pricing discrete time American or Bermudan options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation, we propose a multilevel low biased estimate for the price of the option. It turns out that the resulting complexity gain can be of order $\varepsilon^{-1}$ with $\varepsilon$ denoting the desired precision. The performance of the proposed multilevel algorithms is illustrated by a numerical example.read more
Citations
More filters
Journal ArticleDOI
Solving high-dimensional optimal stopping problems using deep learning
TL;DR: An algorithm is proposed for solving high-dimensional optimal stopping problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations of an optimal exercise strategy and the price of the considered option.
Journal ArticleDOI
Convergence of a least‐squares monte carlo algorithm for american option pricing with dependent sample data
TL;DR: New estimates on the stochastic component of the error of the Longstaff–Schwartz algorithm are proved whenever the approximation architecture is any uniformly bounded set of L2 functions of finite Vapnik–Chervonenkis dimension (VC‐dimension), but in particular need not necessarily be either convex or closed.
Posted Content
Kriging Metamodels and Experimental Design for Bermudan Option Pricing
TL;DR: Two new strategies for the numerical solution of optimal stopping problems within the Regression Monte Carlo (RMC) framework of Longstaff and Schwartz are investigated and stochastic kriging (Gaussian process) meta-models for fitting the continuation value are proposed.
Journal ArticleDOI
Solving high-dimensional optimal stopping problems using deep learning
TL;DR: In this article, the authors propose an algorithm for solving high-dimensional optimal stopping problems, which is based on deep learning and computes both approximations of an optimal exercise strategy and the price of the considered option.
References
More filters
Book
Monte Carlo Methods in Financial Engineering
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.
Journal ArticleDOI
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.
Valuing American Options by Simulation: A Simple Least-Squares Approach - eScholarship
TL;DR: In this article, a simple yet powerful new approach for approximating the value of American options by simulation is presented, based on the use of least squares to estimate the conditional expected payoff to the optionholder from continuation.
Journal ArticleDOI
Multilevel Monte Carlo Path Simulation
TL;DR: It is shown that multigrid ideas can be used to reduce the computational complexity of estimating an expected value arising from a stochastic differential equation using Monte Carlo path simulations.
Journal ArticleDOI
Regression methods for pricing complex American-style options
John N. Tsitsiklis,B. Van Roy +1 more
TL;DR: A simulation-based approximate dynamic programming method for pricing complex American-style options, with a possibly high-dimensional underlying state space, and a related method which uses a single (parameterized) value function, which is a function of the time-state pair.