A Note on Average Rate Options with Discrete Sampling

The authors model the fair value of average rate financial options as the solution of partial differential equations. When the average is sampled discretely the equation to be solved is the Black–Scholes equation with the measure of the average-to-date being a parameter in the problem and a jump condition across sampling dates. The authors show how to derive explicit results for the value of average rate options when the average is measured arithmetically. When the average is measured geometrically the problem must be solved numerically.