LookbackBS {QFRM} | R Documentation |
Lookback option valuation with Black-Scholes (BS) model
Description
Calculates the price of a lookback option using a BSM-adjusted algorithm; Carries the assumption that the asset price is observed continuously.
Usage
LookbackBS(o = OptPx(Opt(Style = "Lookback")), Smax = 50, Smin = 50,
Type = c("Floating", "Fixed"))
Arguments
o |
An object of class |
Smax |
The maximum asset price observed to date. |
Smin |
The minimum asset price observed to date. |
Type |
Specifies the Lookback option as either Floating or Fixed- default argument is Floating. |
Details
To price the lookback option, we require the Smax/Smin, S0, r, q, vol, and ttm arguments from the object classes defined in the package. An example of a complete OptLookback option object can be found in the examples.
Value
An original OptPx
object with PxBS
field as the price of the option
and user-supplied Smin
, Smax
, and Type
lookback parameters attached.
Author(s)
Richard Huang, Department of Statistics, Rice University, Spring 2015
References
Hull, J.C., Options, Futures and Other Derivatives, 9ed, 2014. Prentice Hall. ISBN 978-0-13-345631-8, http://www-2.rotman.utoronto.ca/~hull/ofod/index.html.
Examples
(o = LookbackBS())$PxBS
LookbackBS(OptPx(Opt(Style = 'Lookback'))) #Uses default arguments
# See Hull 9e Example 26.2, p.608; gives price of 7.79
o = Opt(Style = 'Lookback', S0 = 50, ttm= .25, Right = "Put")
o = OptPx(o,r = .1, vol = .4)
o = LookbackBS(o, Type = "Floating")
# See Hull 9e Example 26.2, p.608; gives price of 8.04
o = Opt(Style = 'Lookback', S0 = 50, ttm= .25, Right = "Call")
o = OptPx(o, r = .1, vol = .4)
o = LookbackBS(o, Type = "Floating")
# Price = 17.7129
o = Opt(Style = 'Lookback', S0 = 50, ttm= 1, Right = "Put", K = 60)
o = OptPx(o,r = .05, q = .02, vol = .25)
o = LookbackBS(o, Type = "Fixed")
# Price = 8.237
o = Opt(Style = 'Lookback', S0 = 50, ttm= 1, Right = "Call", K = 55)
o = OptPx(o,r = .1, q = .02, vol = .25)
o = LookbackBS(o, Type = "Fixed")