The duration of option portfolios
Duration is a value-weighted measure of average maturity which is commonly associated with portfolios of fixed-income securities. However, the concept finds application in option pricing theory also. This article shows that if options are valued by the Black (1976) formula and a comparative-statics methodology is employed, then the interest rate sensitivity of a portfolio of European options is equal to its duration. If the options are instead valued through the Black-Scholes (1973) formula, then the interest rate sensitivity is equal to only the ‘bond-equivalent duration’ inherent in a dynamic replication strategy for the option portfolio.