Modelling Callable Annuity Bonds with Interest-Only Optionality

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 is introduced. Next an algorithm for pricing callable annuities with I-O optionality using the finite difference methodology, is formulated. This is then used to investigate optimal strategies of I-O bonds and impacts on prices from the I-O optionality. It is found that the I-O feature necessitates a simultaneous valuation of all elements of the callable I-O bond. 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 heterogenous prepayment decisions is incorporated into the framework. The model is extended to model heterogeneity in the I-O exercise decisions. The incorporation of heterogeneity in borrower decisions is found to lead to reasonable causalities.