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Classification of two-and three-factor time-homogeneous separable LMMs

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Gogala, Jaka and Kennedy, Joanne E. (2017) Classification of two-and three-factor time-homogeneous separable LMMs. International Journal of Theoretical and Applied Finance, 20 (2). 1750021. doi:10.1142/S0219024917500212 ISSN 0219-0249.

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Official URL: http://dx.doi.org/10.1142/S0219024917500212

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Abstract

The flexibility of parametrizations of the LIBOR market model (LMM) comes at a cost, namely the LMM is high-dimensional, which makes it cumbersome to use when pricing derivatives with early exercise features. One way to overcome this issue for short- and medium-term time horizons is by imposing the separability condition on the volatility functions and approximating the model using a single time-step approximation.

In this paper, we examine the flexibility of separable LMMs under the relaxed assumption that the driving Brownian motions can be correlated. In particular, we are interested in how the separability condition interacts with time-homogeneity, a desirable property of a LMM. We show that the two concepts can be related using a Levi-Civitá equation and provide a characterization of two- and three-factor separable and time-homogeneous LMMs and show that they are of practical interest. The results presented in this paper are also applicable to local-volatility LMMs. These separable volatility structures can be used for the driver of a two- or three-dimensional Markov-functional model — in which case no (single time-step) approximation is needed and the resultant model is both time-homogeneous and arbitrage-free.

Item Type: Journal Article
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Statistics
Library of Congress Subject Headings (LCSH): LIBOR market model, Markov processes
Journal or Publication Title: International Journal of Theoretical and Applied Finance
Publisher: World Scientific Publishing Co. Pte. Ltd.
ISSN: 0219-0249
Official Date: 13 March 2017
Dates:
DateEvent
13 March 2017Available
18 January 2017Accepted
Volume: 20
Number: 2
Article Number: 1750021
DOI: 10.1142/S0219024917500212
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
Date of first compliant deposit: 24 April 2017
Date of first compliant Open Access: 24 April 2017

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