Nonanalytic behaviour in a log-normal Markov functional model

Details Nonanalytic behaviour in a log-normal Markov functional model Nonanalytic behaviour in a log-normal Markov functional model

2011-04-02

arxiv.org/abs/1104.0322v3

Economy

Quantitative Finance

Computational Finance

10 pages, 5 figures

Scientific paper

In a previous paper it was shown that a Markov-functional model with log-normally distributed rates in the terminal measure displays nonanalytic behaviour as a function of the volatility, which is similar to a phase transition in condensed matter physics. More precisely, certain expectation values have discontinuous derivatives with respect to the volatility at a certain critical value of the volatility. Here we discuss the implications of these results for the pricing of interest rates derivatives. We point out the presence of nonanalyticity effects in other quantities of the model, focusing on the properties of the Libor probability distribution function in a measure in which it is simply related to caplet prices. We show that the moments of this distribution function have nonanalytic dependence on the volatility, which are also similar to a phase transition. We study in some detail the pricing of caplets on Libor rates and Libor payments in arrears, and show that the convexity adjustment for the latter is also nonanalytic in the model volatility.

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