LookbackBS: Lookback option valuation with Black-Scholes (BS) model

In QFRM: Pricing of Vanilla and Exotic Option Contracts

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.

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")

Example output

[1] 16.61741
$S0
[1] 50

$ttm
[1] 2

$K
[1] 52

$Style
$Style$Name
[1] "Lookback"

$Style$Vanilla
[1] FALSE

$Style$Exotic
[1] TRUE

$Style$European
[1] FALSE

$Style$American
[1] FALSE

$Style$Asian
[1] FALSE

$Style$Binary
[1] FALSE

$Style$AverageStrike
[1] FALSE

$Style$Barrier
[1] FALSE

$Style$Chooser
[1] FALSE

$Style$Compound
[1] FALSE

$Style$DeferredPayment
[1] FALSE

$Style$ForeignEquity
[1] FALSE

$Style$ForwardStart
[1] FALSE

$Style$Gap
[1] FALSE

$Style$HolderExtendible
[1] FALSE

$Style$Ladder
[1] FALSE

$Style$Lookback
[1] TRUE

$Style$MOPM
[1] FALSE

$Style$Perpetual
[1] FALSE

$Style$Quotient
[1] FALSE

$Style$Rainbow
[1] FALSE

$Style$Shout
[1] FALSE

$Style$SimpleChooser
[1] FALSE

$Style$VarianceSwap
[1] FALSE


$Right
$Right$Name
[1] "Call"

$Right$Call
[1] TRUE

$Right$Put
[1] FALSE

$Right$Other
[1] FALSE

$Right$SignCP
[1] 1


$Curr
[1] "$"

$ContrSize
[1] 100

$SName
[1] "A stock share"

$SSymbol
[1] ""

$r
[1] 0.05

$q
[1] 0

$rf
[1] 0

$vol
[1] 0.3

$NSteps
[1] 3

$u
[1] 1.277556

$d
[1] 0.7827445

$dt
[1] 0.6666667

$a
[1] 1.033895

$p
[1] 0.5075682

$SYld
[1] 0.05

$DF_ttm
[1] 0.9048374

$DF_dt
[1] 0.9672161

$Smax
[1] 50

$Smin
[1] 50

$Type
[1] "Floating"

$PxBS
[1] 16.61741

attr(,"class")
[1] "Opt"   "OptPx"

QFRM documentation built on May 2, 2019, 8:26 a.m.