Not Available for Download

European Compound Options Written on Perpetual American Options

Posted: 17 Nov 2010  

Gaia Barone

LUISS Guido Carli, Department of Business and Management

Date Written: November 1, 2010

Abstract

Perpetual American warrants have been traded on the stock exchanges or over the counter at least since 1929, as it is emphasized in several of the "most-read" finance books. The first rational model to evaluate perpetual American call options appeared as early as 1965, when McKean (Samuelson’s Appendix) derived a closed-form valuation formula under the now-standard hypothesis of a geometric Brownian motion for the price of the underlying stock. A formula for perpetual American put options was later derived by Merton (1973) for the no-dividend case.

In this paper, I review the formulas for perpetual American call and put options, written on dividend paying stocks, and show that they can be expressed in a more intuitive way by defining the "distance to exercise". Then, by using perpetual first-touch digitals, I derive a put-call parity for perpetual American options. Finally, I present formulas for European compound options written on perpetual American options. These formulas use the results for barrier options obtained by Rubinstein and Reiner. I highlight that these authors "implicitly" derived the value of finite-maturity first-touch digitals, which generalize the McKean-Samuelson-Merton formulas for perpetual American options.

Keywords: perpetual options, compound options, barrier options, first-touch digitals, Greeks, put-call parity, distance to exercise, time to exercise

JEL Classification: G13

Suggested Citation

Barone, Gaia, European Compound Options Written on Perpetual American Options (November 1, 2010). Journal of Derivatives, Vol. 20, No. 3: pp. 61-74, Spring 2013. Available at SSRN: https://ssrn.com/abstract=1709288 or http://dx.doi.org/10.2139/ssrn.1709288

Gaia Barone (Contact Author)

LUISS Guido Carli, Department of Business and Management ( email )

Viale Romania, 32
Rome, Rome 00197
Italy

Paper statistics

Abstract Views
854