An extendible option which, at the initial maturity date, can be exercised as a plain vanilla European option if it is in the money; otherwise (when the option is out-of-the-money), it can be extended as a new European option with a farther maturity date and a new underlying asset (the strike prices can be different before and after the extension. All other elements, except the underlying, are fixed). In other words, and unlike ordinary extendible options, the underlying of external extendible options can be replaced by another over the extended period. In this sense, an external extendible option is similar to a multi-asset option.