We provide an analytic valuation framework to value second mortgages and first lien mortgages when owners can take out a second lien. We then use the framework to value mortgage-backed securities (MBS) and, in particular, quantify the greater risk associated with MBS backed by first liens that...

The extension of the Black-Scholes option pricing theory to the valuation of barrier options is reconsidered. Working in the binomial framework of CRR we show how various types of barrier options can be priced either by backward induction or by closed binomial formulas. We also consider...