@MISC{Brace_non-bushytrees, author = {Alan Brace}, title = {Non-Bushy Trees For Gaussian Hjm And Lognormal Forward Models}, year = {} }

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Abstract

For an arbitrary number of factors and with a quite general volatility structure, a method is given for constructing non-bushy (recombining) trees in the Gaussian HJM and LogNormal Forward models. INTRODUCTION It is easy to build a joined tree to value American swaptions and other path dependent options when the interest rate model is Markov in the spot. When it is not, two approaches have so far been available; for each instrument approximate the volatility with a spot Markov model and construct a joined tree; build a bushy tree of twelve or more steps depending on the speed of the computer. Both methods price individual contracts accurately, but are inappropriate to risk-manage large portfolios. The former leads to a proliferation of trees, because each instrument and maturity requires a different tree, while the latter cannot be regarded as robust when calculation times increase exponentially. This article describes a method of constructing a one-dimensional non-bushy tree, which ...