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European Compound Options Written
on Perpetual American Options

Gaia Barone
The Journal of Derivatives Spring 2013, 20 (3) 61-74; DOI: https://doi.org/10.3905/jod.2013.20.3.061
Gaia Barone
is an adjunct professor and research fellow at LUISS Guido Carli University of Rome in Italy.
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  • For correspondence: gbarone@luiss.it
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Abstract

It may seem counterintuitive, but valuing “perpetual” options, with infinite maturity, can be easier than pricing those that expire at a fixed date. At least Samuelson found it so in 1965. In this article, Barone extends the valuation models for perpetual options to cover American calls and puts on dividend-paying stocks, and European options written on these infinite maturity contracts. Formulas for the Greek letter risks are presented, as well as an analysis of how put-call parity works for them. Along the way, additional results are developed for first-touch digital options, both perpetual and finite maturity.

TOPICS: Options, quantitative methods

  • © 2013 Pageant Media Ltd
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The Journal of Derivatives: 20 (3)
The Journal of Derivatives
Vol. 20, Issue 3
Spring 2013
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European Compound Options Written
on Perpetual American Options
Gaia Barone
The Journal of Derivatives Feb 2013, 20 (3) 61-74; DOI: 10.3905/jod.2013.20.3.061

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European Compound Options Written
on Perpetual American Options
Gaia Barone
The Journal of Derivatives Feb 2013, 20 (3) 61-74; DOI: 10.3905/jod.2013.20.3.061
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  • Article
    • Abstract
    • DYNAMICS OF STOCK AND OPTIONS PRICES
    • Dynamics of the Price of a Perpetual Derivative
    • Black-Scholes-Merton Differential Equation
    • PERPETUAL CALL
    • PERPETUAL PUT
    • DISTANCE TO EXERCISE
    • GREEKS OF PERPETUAL AMERICAN OPTIONS
    • PERPETUAL FIRST-TOUCH DIGITALS
    • PUT-CALL PARITY FOR PERPETUAL AMERICAN OPTIONS
    • EUROPEAN OPTIONS ON PERPETUAL AMERICAN OPTIONS
    • FINITE-MATURITY FIRST-TOUCH DIGITALS
    • CONCLUSIONS
    • ENDNOTES
    • REFERENCES
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