Compound Option

Explained:

A compound option is an option on an option. In the simplest incarnation, compound options take four basic forms:

call on a call,

call on a put,

put on a call,

put on a put.

They are specified with two strike prices and two expiration dates—one of each for the compound option and one of each for the underlying option. There are two possible option premiums. One is paid up front for the compound option. The other is paid for the underlying option in the event that the compound option is exercised. Generally, the premium for the compound option is modest. However, if the compound option is exercised, the combined premiums will exceed what would have been the premium for purchasing the underlying option outright at the start.

Compound option values are extremely sensitive to the volatility of volatility. Analytic formulas by Geske (1979), Hodges and Selby (1987) and Rubinstein (1991) incorporate the Black-Scholes assumption of constant volatility, so they tend to significantly undervalue the options. Research into pricing methodologies is ongoing.

Compound options are also bundled with vanilla options, allowing for the option to be extended beyond its original expiration date. Two forms of such extendible options are:

holder extendible options grant the holder the right to pay an additional premium at the option's original expiration in order to postpone the expiration date.

writer extendible options extend automatically at the original expiration date if some condition, such as the option being out-of-the-money, is met. No additional premium is paid at the time of extension.

With either form, the extended option may have different provisions, such as a different strike, from the original option.

Analytic formulas for pricing extendible options are presented by Longstaff (1990). See also the treatment in Haug (1997). These formulas also incorporate a constant volatility assumption, so they tend to undervalue the options.