QuotientMC: Quotient option valuation via Monte Carlo (MC) model

In QFRM: Pricing of Vanilla and Exotic Option Contracts

Description

Calculates the price of a Quotient option using Monte-Carlo simulations.

Usage

QuotientMC(o = OptPx(Opt(Style = "Quotient")), S0_2 = 100, NPaths = 5)

Arguments

o	The OptQuotient option object to price.
S0_2	The spot price of the second underlying asset.
NPaths	Number of monte-carlo simulations to run. Larger number of trials lower variability at the expense of computation time.

Details

The Monte-Carlo simulations assume the underlying price undergoes Geometric Brownian Motion (GBM). Payoffs are discounted at risk-free rate to price the option. A thorough understanding of the object class construction is recommended. Please see OptPx, Opt for more information.

Value

An original OptPx object with Px.MC field as the price of the option and user-supplied S0_2, NPaths parameters attached.

Author(s)

Richard Huang, Department of Statistics, Rice University, Spring 2015

References

http://www.investment-and-finance.net/derivatives/q/quotient-option.html

Examples

(o = QuotientMC())$PxMC #Default Quotient option price.

o = OptPx(Opt(S0=100, ttm=1, K=1.3), r=0.10, q=0, vol=0.1)
(o = QuotientMC(o, S0_2 = 180, NPaths=5))$PxMC

QuotientMC(OptPx(Opt()), S0_2 = 180, NPaths=5)

QuotientMC(OptPx(), S0_2 = 201, NPaths = 5)

QuotientMC(OptPx(Opt(S0=500, ttm=1, K=2)), S0_2 = 1000, NPaths=5)

Example output

[1] 0
[1] 0.553943
$S0
[1] 50

$ttm
[1] 2

$K
[1] 52

$Style
$Style$Name
[1] "European"

$Style$Vanilla
[1] TRUE

$Style$Exotic
[1] FALSE

$Style$European
[1] TRUE

$Style$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] 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

$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

$S0_2
[1] 180

$NPaths
[1] 5

$PxMC
[1] 0

attr(,"class")
[1] "Opt"   "OptPx"
$S0
[1] 50

$ttm
[1] 2

$K
[1] 52

$Style
$Style$Name
[1] "European"

$Style$Vanilla
[1] TRUE

$Style$Exotic
[1] FALSE

$Style$European
[1] TRUE

$Style$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] 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

$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

$S0_2
[1] 201

$NPaths
[1] 5

$PxMC
[1] 0

attr(,"class")
[1] "Opt"   "OptPx"
$S0
[1] 500

$ttm
[1] 1

$K
[1] 2

$Style
$Style$Name
[1] "European"

$Style$Vanilla
[1] TRUE

$Style$Exotic
[1] FALSE

$Style$European
[1] TRUE

$Style$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] 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

$rf
[1] 0

$vol
[1] 0.3

$NSteps
[1] 3

$u
[1] 1.18911

$d
[1] 0.8409651

$dt
[1] 0.3333333

$a
[1] 1.016806

$p
[1] 0.5050806

$SYld
[1] 0.05

$DF_ttm
[1] 0.9512294

$DF_dt
[1] 0.9834715

$S0_2
[1] 1000

$NPaths
[1] 5

$PxMC
[1] 0.311187

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

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