The vauation of floating rate mortgages : the case of adjustable rate mortgages (ARMs), the valuation of ARMs indexed to the FCB lending rate

Abstract

This dissertation attempts to investigate a consistent valuation algorithm for the valuation of adjustable rate mortgages indexed to the ECB lending rate. More specifically, the option of the mortgage holder to prepay his obligation at any point during the life of the loan is examined. Due to the fact that mortgage cash flows depend on the path that the interest rates will follow during the life of the loan, the Monte – Carlo simulation technique was used as a basic valuation tool. The market rate was assumed to follow the stochastic process introduced by Cox, Ingersoll and Ross (1985) while the index rate was assumed to have a linear relationship with the market rate and the first lag of the index rate. In order to value the prepayment option, the methodology used was similar to the one proposed by Longstaff and Schwartz (2001) for the valuation of American options with the use of Monte – Carlo simulation. The main conclusions of the empirical results are: a) there is a positive relationship between the value of the equivalent bond (the stream of promised payments, with no prepayment option) and the value of the prepayment option, b) the value of the prepayment option is critically dependent on the interaction between contract features, especially caps and margin levels. More specifically, caps pose an upper boundary on the prepayment option values while margins significantly increase the prepayment option value as a percentage of the remaining principal amount, c) the lag in the adjustment of the index rate with the market rate has a significant effect on the value of the prepayment option.