Perpetual option valuation via Black-Scholes (BS) model

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Description

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.

Usage

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

Arguments

o

AN object of class OptPx

Value

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

Author(s)

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

References

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

Examples

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#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

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