An analysis of a least squares regression method for American option pricing

This paper describes an American Monte Carlo approach for obtaining fast and accurate exercise policies for pricing of callable LIBOR Exotics (e.g., Bermudan swaptions) in the LIBOR market model using the Stochastic Grid Bundling Method (SGBM). SGBM is a bundling and regression based Monte Carlo method where the continuation value is projected onto a space where the distribution is known. We also demonstrate an algorithm to obtain accurate and tight lower-upper bound values without the need for nested Monte Carlo simulations.

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“…A rigorous mathematical justification and proof of the almost sure convergence of the method can be found in Clement et al (2002).…”

Section: The Least Squares Methodsmentioning

confidence: 99%

Fast and Accurate Exercise Policies for Bermudan Swaptions in Libor Market Model

Karlsson¹,

Jain²,

Oosterlee

2013

SSRN Journal

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“…Clément, Lamberton and Protter (2002) were first who proved the convergence of the Longstaff-Schwartz algorithm. Glasserman and Yu (2005) have shown that the number of Monte Carlo paths has to be exponential in the number of basis functions used for regression in order to ensure convergence.…”

Section: Convergence Analysis Of Regression Methodsmentioning

confidence: 99%

“…Convergence proofs for global estimators are more delicate and usually impose rather strong assumptions on C r and the underlying Markov process X r . For the standard Bermudan stopping problem (f r ≡ 0, ϕ ≡ 1) we refer to Clément, Lamberton and Protter (2002), Egloff (2005) and Egloff, Kohler and Todorovic (2007). The global regression procedures in the next two sections are in some sense a generalization of the methods of Tsitsiklis and Van Roy (1999) and Longstaff and Schwartz (2001), respectively, to optimal control problems.…”

Section: Global Regression Estimatorsmentioning

confidence: 99%

Regression Methods for Stochastic Control Problems and Their Convergence Analysis

Belomestny¹,

Kolodko²,

Schoenmakers³

2010

SIAM J. Control Optim.

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In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particulary useful for problems with high-dimensional state space and complex dependence structure of the underlying Markov process with respect to some control. The main idea of the algorithms is to simulate a set of trajectories under some reference measure P * and to use a dynamic program formulation combined with fast methods for approximating conditional expectations and functional optimizations on these trajectories. Theoretical properties of the presented algorithms are investigated and convergence to the optimal solution is proved under mild assumptions. Finally, we present numerical results showing the efficiency of regression algorithms in a case of a highdimensional Bermudan basket options, in a model with a large investor and transaction costs.

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“…To summarize the current state-ofthe-art in this field, let us mention the work of Clément et al (2002) and Egloff (2005) on the Longstaff-Schwartz scheme and Bouchard and Touzi (2004), Bally and Pagès (2003) and Gobet et al (2005) on numerical methods for backward SDEs. For the LS scheme it has been shown that the use of optimal-stopping-time iteration in (29) is consistent, namely that for a fixed N B the asymptotic sampling error as N → ∞ has mean zero and Gaussian distribution (Clément et al 2002). This result was recently improved by Egloff (2005) who showed that the L 2 -sampling error for a single optimal stopping problem and fixed ∆t is O(log N · N −1 ).…”

Section: Projection Errormentioning

confidence: 99%

Pricing Asset Scheduling Flexibility using Optimal Switching

Carmona

Ludkovski

2008

Applied Mathematical Finance

108

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We study the financial engineering aspects of operational flexibility of energy assets. The current practice relies on a representation that uses strips of European spark-spread options, ignoring the operational constraints. Instead, we propose a new approach based on a stochastic impulse control framework. The model reduces to a cascade of optimal stopping problems and directly demonstrates that the optimal dispatch policies can be described with the aid of 'switching boundaries', similar to the free boundaries of standard American options. Our main contribution is a new method of numerical solution relying on Monte Carlo regressions. The scheme uses dynamic programming to efficiently approximate the optimal dispatch policy along the simulated paths. Convergence analysis is carried out and results are illustrated with a variety of concrete examples. We benchmark and compare our scheme to alternative numerical methods.

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An analysis of a least squares regression method for American option pricing

Cited by 288 publications

References 9 publications

Fast and Accurate Exercise Policies for Bermudan Swaptions in Libor Market Model

Fast and Accurate Exercise Policies for Bermudan Swaptions in Libor Market Model

Regression Methods for Stochastic Control Problems and Their Convergence Analysis

Pricing Asset Scheduling Flexibility using Optimal Switching

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