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The Valuation of Interest Rate Digital Options and Range Notes Revisited
Author(s) -
Navatte Patrick,
QuittardPi François
Publication year - 1999
Publication title -
european financial management
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.311
H-Index - 64
eISSN - 1468-036X
pISSN - 1354-7798
DOI - 10.1111/1468-036x.00103
Subject(s) - interest rate , range (aeronautics) , valuation (finance) , rendleman–bartter model , economics , value (mathematics) , nominal interest rate , econometrics , forward rate , numéraire , liberian dollar , term (time) , short rate , international fisher effect , mathematical economics , mathematics , yield curve , real interest rate , statistics , accounting , finance , materials science , physics , quantum mechanics , composite material
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 a prespecified interest rate times the number of days the reference interest rate lies inside a corridor.