VALUES OF MORTGAGES WITH TOP-UP PAYMENT OPTIONS

The right of lenders to request for top-ups of negative equity when the property value falls below the loan outstanding is a little known, yet widely adopted provision in mortgage documents in many Asian markets. We analyze the effect of the top-up option by appealing to a contingent claim framework. Specifically, we model the top-up option as a synthetic option comprising a long put to request for a top-up, a short put that cancels out the first option in the event of a default, and a binary put option once triggered will yield a value equivalent to the difference between the mortgage outstanding and the property value. The results of comparative analyses show that the lender's right to request for top-ups is valuable when the negative mortgage equity increases, especially in a market where price is highly volatile. The top-up clause fundamentally affects the mortgage values for both the borrower and the lender. We show that lender's inaction by not calling for top-ups when negative mortgage equity occurs is suboptimal. On the other hand, the lenders' exercise of the in-the-money top-up options may lead to early default by the mortgagor. This is one of the reasons why lenders exercise this option only very sparingly in practice. This mortgage design has economic value to the lenders, it is, however, not optimal in time of volatile market. The policy implication of the findings is that the sub-optimal top-up feature should be removed from the mortgage contract, and it will not severely jeopardize the lender's ability to enforce payments in the mortgages.

Issues in the acquisition of the Sesotho tonal system

ABSTRACTThis paper examines the acquisition of the grammatical tone system of Sesotho, a southern Bantu language where tone sandhi is rich, and where surface and underlying representations are often quite distinct. Results of the longitudinal case study show that rule-assigned tone on subject markers is generally marked appropriately by age two. In contrast, underlying tonal representations on verb roots are learned gradually over time, showing an early Default High tone pattern. The study also finds that, while some tone sandhi rules are in the process of being acquired between 2;6 and 3;0, problems in the mapping between tonal representations and segments persist. The paper raises methodological and theoretical issues not only for the acquisition of tonal systems, but for the acquisition of phonology in general.