Embedded interest rate collars in household loan contracts

Abstract

This thesis work studies the problem of pricing an interest rate collar embedded into a regular household loan contract (or more specifically into a mortgage). Because the collar is embedded into another financial contract sharing its dynamics, it is argued that the value of the embedded derivatives contract cannot equal the value of a vanilla interest rate collar. This is because of the risk of early loan cancellations (or prepayments) that – unlike in a vanilla collar – do not trigger an obligation for the borrower to compensate the possible negative market value of the embedded collar structure. Therefore, the majority of the work was devoted to assess ways to value the risk of prepayments and to build an interest rate model that could be used to evaluate the – essentially path-dependent – additional option. The additional call option was evaluated with an option-theoretic model and an econometric model which represent the two different families of prepayment models. The option-theoretic model with its assumption of pure rational behaviour among the mortgagors was used to evaluate the upper bound of the call option. The econometric model with its contrary assumption of a group of heterogeneously behaving mortgagors prepaying at different times was supposed to give the lower bound. However, the econometric model adopted from the mortgage-backed securities markets gave results that were inconsistent with the premise, and hence only the upper bound of the call option was successfully calculated.