Longstaff-Schwartz, Effective Model Dimensionality and Reducible Markov-Functional Models

29 Pages Posted: 6 Mar 2005

See all articles by Phil J. Hunt

Phil J. Hunt

WestLB - Global Derivatives and Fixed Income Markets; Citigroup - Global Corporate and Investment Banking Group (GCIB)

Joanne Kennedy

University of Warwick - Department of Statistics

Date Written: February 26, 2005

Abstract

The popularity of the so-called Market Models has led researchers and practitioners to ask two important questions about modelling interest-rate derivatives. The first (and highly contentious) question is, how many stochastic drivers are needed to value accurately any given derivative? The second, which arises because of the high dimensionality of Market Models, even those with a small number of stochastic drivers, is how can callable products be valued using Monte Carlo simulation?

In this paper we consider the Longstaff-Schwartz algorithm, an effective algorithm developed to answer the second of these questions, and in so doing we shed light on the first of these questions. We show that the success of the Longstaff-Schwartz algorithm for high-dimensional models demonstrates that, in a way we make precise, low-dimensional models are sufficient, but that in another sense the higher dimensionality still plays a part.

Using the insight gained from this analysis we go on to develop models which have these desirable properties - high dimensionality and accurate calibration properties on the one hand, but the ability to collapse the models onto lower-dimensional 'core' models for the purposes of valuing callable derivatives. The core models that we develop are Markovian and can thus be implemented efficiently using lattice methods, avoiding the need for more costly Monte Carlo simulation.

Keywords: Markov-functional, Callable, Interest-rate models

Suggested Citation

Hunt, Phil James and Hunt, Phil James and Kennedy, Joanne E., Longstaff-Schwartz, Effective Model Dimensionality and Reducible Markov-Functional Models (February 26, 2005). Available at SSRN: https://ssrn.com/abstract=627921 or http://dx.doi.org/10.2139/ssrn.627921

Phil James Hunt

WestLB - Global Derivatives and Fixed Income Markets ( email )

Woolgate Exchange
25 Basinghall Street
London, EC2V 5HA
United Kingdom

Citigroup - Global Corporate and Investment Banking Group (GCIB) ( email )

Citigroup Centre
Canada Square, Canary Wharf
London, E14 5LB
United Kingdom

Joanne E. Kennedy (Contact Author)

University of Warwick - Department of Statistics ( email )

Coventry CV4 7AL
United Kingdom

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