PerpetualBS: Perpetual option valuation via Black-Scholes (BS) model
In QFRM: Pricing of Vanilla and Exotic Option Contracts

Description Usage Arguments Value Author(s) References Examples

An exotic option is an option which has features making it more complex than commonly traded options. A perpetual option is non-standard financial option with no fixed maturity and no exercise limit. While the life of a standard option can vary from a few days to several years, a perpetual option (XPO) can be exercised at any time. Perpetual options are considered an American option. European options can be exercised only on the option's maturity date.

1	PerpetualBS(o = OptPx(Opt(Style = "Perpetual"), q = 0.1))

`o`	AN object of class `OptPx`

A list of class Perpetual.BS consisting of the input object OptPx

Kim Raath, Department of Statistics, Rice University, Spring 2015.

Chi-Guhn Lee, The Black-Scholes Formula, Courses, Notes, Note2, Sec 1.5 and 1.6 http://www.mie.utoronto.ca/courses/mie566f/materials/note2.pdf

#Perpetual American Call and Put
#Verify pricing with \url{http://www.coggit.com/freetools}
(o <- PerpetualBS())$PxBS # Approximately valued at $8.54

#This example should produce approximately $33.66
o = Opt(Style="Perpetual", Right='Put', S0=50, K=55)
o = OptPx(o, r = .03, q = 0.1, vol = .4)
(o = PerpetualBS(o))$PxBS

#This example should produce approximately $10.87
o = Opt(Style="Perpetual", Right='Call', S0=50, K=55)
o = OptPx(o, r = .03, q = 0.1, vol = .4)
(o <- PerpetualBS(o))$PxBS