The Valuation of Interest Rate Digital Options and Range Notes Revisited

The aim of this paper is to value interest rate structured products in a simpler and more intuitive way than Turnbull(1995). Considering some assumptions with respect to the evolution of the term structure of interest rates, the price of a European interest rate digital call option is given. Recall it is a contract designed to pay one dollar at maturity if a reference interest rate is above a prespecified level (the strike), and zero in all the others cases. Combining two options of this type enables us to value a European range digital option. Then using a one factor linear Gaussian model and the new well-known change of numeraire approach, a closed-form formula is found to value range notes which pay at the end of each defined period, a sum equal to prespecified interest rate times the number of days the reference interest rate lies inside a corridor