This article introduces extendible options, and provides pricing free spreadsheets. Extendible options are a type of compound option and allow the life of the option to be extended beyond the original maturity date.
A holder-extendible option can be extended by the holder. However, the holder must pay a premium for the privilege.
A writer-extendible option can be extended by the writer (i.e. the issuing organization). In this case, a premium is not paid by the writer to the holder. Only out-of-the-money options are often automatically extended at maturity.
Both forms have two strike prices.
Longstaff (1990) derives closed-form expressions to price both variants.