Markov Market Model Consistent with Cap Smile

Balland, P and Hughston, L P. 2000. Markov Market Model Consistent with Cap Smile. International Journal of Theoretical and Applied Finance, 3(2), 161 -181. ISSN 0219-0249 [Article]

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Abstract or Description

New interest rate models have emerged recently in which distributional assumptions are made directly on financial observables. In these "Market Models" the Libor rates have a log-normal distribution in the corresponding forward measure, and caps are priced according to the Black–Scholes formula. These models present two disadvantages. First, Libor rates do not in reality have a log-normal distribution since the implied volatility of a cap depends typically on the strike. Second, these models are difficult to use for pricing derivatives other than caps. In this paper, we extend these models to allow for a broader class of Libor rate distributions. In particular, we construct multi-factor Market Models that are consistent with an initial cap smile surface, and have the useful feature of exhibiting Markovian Libor rates. We show that these Markov Market Models can be used relatively easily to price complex Libor derivatives, such as Bermudan swaptions, captions or flexi-caps, by construction of a tree of Libor rates.

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Interest rate term structure, HJM theory, market models, BGM models, implied libor trees

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1 April 2000Published
1 April 2000Accepted

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Date Deposited:

04 Feb 2022 12:37

Last Modified:

04 Feb 2022 22:33

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Yes, this version has been peer-reviewed.


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