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EnglishPerpetual 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.
| Titolo: | European Compound Options Written on Perpetual American Options |
| Autori: | |
| Data di pubblicazione: | 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. |
| Handle: | http://hdl.handle.net/11385/130997 |
| Appare nelle tipologie: | 05.1 - Working Paper |
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