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]

No full text available

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.

Item Type:

Article

Identification Number (DOI):

https://doi.org/10.1142/S0219024900000085

Keywords:

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

Departments, Centres and Research Units:

Computing

Dates:

DateEvent
1 April 2000Published
1 April 2000Accepted

Item ID:

31375

Date Deposited:

04 Feb 2022 12:37

Last Modified:

04 Feb 2022 22:33

Peer Reviewed:

Yes, this version has been peer-reviewed.

URI:

https://research.gold.ac.uk/id/eprint/31375

Edit Record Edit Record (login required)