Compound Option

Explained: compound option extendible option holder extendible option writer extendible option

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.

Related Internal Links
chooser option A derivative that converts to a vanilla put or a vanilla call at the holder's choice. derivative instrument An instrument which derives its value from the value of other financial instruments. Article includes a list of vanilla and exotic derivatives. option pricing theory The body of financial theory used by financial engineers to value options and other derivative instruments.
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Related Books
Haug (1997) and Bryis et al (1998) describes classic pricing methodologies. Taleb (1996) has a chapter on compound and chooser options, primarily from a trading and dynamic hedging perspective. Das (2004) also discusses compound options. Complete Guide to Option Pricing Formulas Espen G. Haug quality   technical   1997   Options, Futures, and Exotic Derivatives quality   technical   1998   Dynamic Hedging Nassim Taleb quality   technical   1996   Swaps/Financial Derivatives Satyajit Das quality   technical   2004
Related Papers
Geske, Robert (1979). The valuation of compound options, Journal of financial economics, 7, 63-81. Hodges, S. D. and M. J. P Selby (1987). On the evaluation of compound options, Management Science, 33 (3), 347-355. Rubinstein, Mark (1991). Double Trouble, Risk, 5 (1), 73. Longstaff, F. A. (1990). Pricing options with extendible maturities: analysis and applications, Journal of Finance, 45 (3), 935-957.
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