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Modelling Callable Annuity Bonds with Interest-Only Optionality

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In this paper an investigation of the pricing of callable annuities with interest-only(I-O) optionality is conducted. First the I-O optionality feature of callable annuities isintroduced. Next an algorithm for pricing callable annuities with I-O optionality usingthe finite difference methodology, is formulated. This is then used to investigate optimalstrategies of I-O bonds and impacts on prices from the I-O optionality. It is found thatthe I-O feature necessitates a simultaneous valuation of all elements of the callable I-Obond. Following this, the Greeks of the I-O bond are investigated. It is found that they are affected by the I-O feature, but only to a limited extent. Finally, a model of heterogenousprepayment decisions is incorporated into the framework. The model is extended to modelheterogeneity in the I-O exercise decisions. The incorporation of heterogeneity in borrowerdecisions is found to lead to reasonable causalities.

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Anders Holst, Morten Nalholm

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