A comparison of Markov-functional and market models : the one-dimensional case
Bennett, Michael N. and Kennedy, J. E.. (2005) A comparison of Markov-functional and market models : the one-dimensional case. The Journal of Derivatives, Vol.13 (No.2). pp. 22-43.
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Official URL: http://dx.doi.org/10.3905/jod.2005.605351
The LIBOR Markov-functional model is an efficient arbitrage-free pricing
model suitable for callable interest rate derivatives. We demonstrate that the
one-dimensional LIBOR Markov-functional model and the separable onefactor
LIBOR market model are very similar. Consequently, the intuition
behind the familiar SDE formulation of the LIBOR market model may be
applied to the LIBOR Markov-functional model.
The application of a drift approximation to a separable one-factor LIBOR
market model results in an approximating model driven by a one-dimensional
Markov process, permitting efficient implementation. For a given parameterisation
of the driving process, we find the distributional structure of this model
and the corresponding Markov-functional model are numerically virtually
indistinguishable for short maturity tenor structures over a wide variety of
market conditions, and both are very similar to the market model. A theoretical
uniqueness result shows that any accurate approximation to a separable
market model that reduces to a function of the driving process is effectively
an approximation to the analogous Markov-functional model. Therefore, our
conclusions are not restricted to our particular choice of driving process. Minor
differences are observed for longer maturities, nevertheless the models
remain qualitatively similar. These differences do not have a large impact
on Bermudan swaption prices.
Under stress-testing, the LIBOR Markov-functional and separable LIBOR
market models continue to exhibit similar behaviour and Bermudan
prices under these models remain comparable. However, the drift approximation
model now appears to admit arbitrage that is practically significant.
In this situation, we argue the Markov-functional model is a more appropriate
choice for pricing.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Markov processes, Interest rates -- Econometric models|
|Journal or Publication Title:||The Journal of Derivatives|
|Publisher:||Institutional Investor * Journals|
|Page Range:||pp. 22-43|
|Access rights to Published version:||Restricted or Subscription Access|
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