BinaryBS: Binary option valuation with Black-Scholes (BS) model

In QFRM: Pricing of Vanilla and Exotic Option Contracts

Description

S3 object pricing model for a binary option. Two types of binary options are priced: 'cash-or-nothing' and 'asset-or-nothing'.

Usage

BinaryBS(o = OptPx(Opt(Style = "Binary")), Q = 1,
  Type = c("cash-or-nothing", "asset-or-nothing"))

Arguments

o	An object of class OptPx
Q	A fixed amount of payoff
Type	Binary option type: 'Cash or Nothing' or 'Asset or Nothing'. Partial names are allowed, eg. 'C' or 'A'

Value

A list of class Binary.BS consisting of the input object OptPx and the appended new parameters and option price.

Author(s)

Xinnan Lu, Department of Statistics, Rice University, Spring 2015

References

Hull, John 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. pp.606-607

Examples

(o = BinaryBS())$PxBS

#This example should produce price 4.33 (see Derivagem, DG201.xls)
o = Opt(Style="Binary", Right='Call', S0=50, ttm=5/12, K=52)
o = OptPx(o, r=.1, vol=.40, NSteps=NA)
(o = BinaryBS(o, Q = 10, Type='cash-or-nothing'))$PxBS

BinaryBS(OptPx(Opt(Style="Binary"), q=.01), Type='asset-or-nothing')
BinaryBS(OptPx(Opt(Style="Binary", S0=100, K=80),q=.01))
o = Opt(Style="Binary", Right="Put", S0=50, K=60)
BinaryBS(OptPx(o,q=.04), Type='asset-or-nothing')

Example output

[1] 0.4275764
[1] 4.339273
$S0
[1] 50

$ttm
[1] 2

$K
[1] 52

$Style
$Style$Name
[1] "Binary"

$Style$Vanilla
[1] FALSE

$Style$Exotic
[1] TRUE

$Style$European
[1] FALSE

$Style$American
[1] FALSE

$Style$Asian
[1] FALSE

$Style$Binary
[1] TRUE

$Style$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] FALSE

$Style$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] 0.01

$rf
[1] 0

$vol
[1] 0.3

$NSteps
[1] 3

$u
[1] 1.277556

$d
[1] 0.7827445

$dt
[1] 0.6666667

$a
[1] 1.027025

$p
[1] 0.4936847

$SYld
[1] 0.04

$DF_ttm
[1] 0.9048374

$DF_dt
[1] 0.9672161

$Q
[1] 1

$Type
[1] "asset-or-nothing"

$isCash
[1] FALSE

$isAsset
[1] TRUE

$PxBS
[1] 30.43781

$S0
[1] 100

$ttm
[1] 2

$K
[1] 80

$Style
$Style$Name
[1] "Binary"

$Style$Vanilla
[1] FALSE

$Style$Exotic
[1] TRUE

$Style$European
[1] FALSE

$Style$American
[1] FALSE

$Style$Asian
[1] FALSE

$Style$Binary
[1] TRUE

$Style$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] FALSE

$Style$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] 0.01

$rf
[1] 0

$vol
[1] 0.3

$NSteps
[1] 3

$u
[1] 1.277556

$d
[1] 0.7827445

$dt
[1] 0.6666667

$a
[1] 1.027025

$p
[1] 0.4936847

$SYld
[1] 0.04

$DF_ttm
[1] 0.9048374

$DF_dt
[1] 0.9672161

$Q
[1] 1

$Type
[1] "cash-or-nothing"

$isCash
[1] TRUE

$isAsset
[1] FALSE

$PxBS
[1] 0.6264202

$S0
[1] 50

$ttm
[1] 2

$K
[1] 60

$Style
$Style$Name
[1] "Binary"

$Style$Vanilla
[1] FALSE

$Style$Exotic
[1] TRUE

$Style$European
[1] FALSE

$Style$American
[1] FALSE

$Style$Asian
[1] FALSE

$Style$Binary
[1] TRUE

$Style$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] FALSE

$Style$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] "Put"

$Right$Call
[1] FALSE

$Right$Put
[1] TRUE

$Right$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] 0.04

$rf
[1] 0

$vol
[1] 0.3

$NSteps
[1] 3

$u
[1] 1.277556

$d
[1] 0.7827445

$dt
[1] 0.6666667

$a
[1] 1.006689

$p
[1] 0.4525853

$SYld
[1] 0.01

$DF_ttm
[1] 0.9048374

$DF_dt
[1] 0.9672161

$Q
[1] 1

$Type
[1] "asset-or-nothing"

$isCash
[1] FALSE

$isAsset
[1] TRUE

$PxBS
[1] 26.20161

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