QFRM (version 1.0.1)

LookbackBS: 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 OptPx.

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.

Value

An original OptPx object with PxBS field as the price of the option and user-supplied Smin, Smax, and Type lookback parameters attached.

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.

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")