Lookback
Description
Create and price a Lookback
instrument object for one or
more Lookback instruments using this workflow:
Use
fininstrument
to create aLookback
instrument object for one or more Lookback instruments.Use
finmodel
to specify aBlackScholes
,Heston
,Bates
, orMerton
model for theLookback
instrument object.Choose a pricing method.
When using a
BlackScholes
model, usefinpricer
to specify aConzeViswanathan
,AssetTree
, orGoldmanSosinGatto
pricing method for one or moreLookback
instruments.When using a
BlackScholes
,Heston
,Bates
, orMerton
model, usefinpricer
to specify anAssetMonteCarlo
pricing method for one or moreLookback
instruments.
For more information on this workflow, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
For more information on the available models and pricing methods for a
Lookback
instrument, see Choose Instruments, Models, and Pricers.
Creation
Syntax
Description
creates a LookbackObj
= fininstrument(InstrumentType
,'Strike
',strike_value,'ExerciseDate
',exercise_date)Lookback
object for one or more Lookback
instruments by specifying InstrumentType
and sets the
properties for the
required name-value pair arguments Strike
and
ExerciseDate
.
The Lookback
instrument supports fixed-strike and
floating-strike lookback options. For more information on a
Lookback
instrument, see More About.
sets optional properties using
additional name-value pairs in addition to the required arguments in the
previous syntax. For example, LookbackObj
= fininstrument(___,Name,Value
)LookbackObj =
fininstrument("Lookback",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"European",'Name',"lookback_option")
creates a Lookback
put option with an European exercise.
You can specify multiple name-value pair arguments.
Input Arguments
InstrumentType
— Instrument type
string with value "Lookback"
| string array with values of "Lookback"
| character vector with value 'Lookback'
| cell array of character vectors with values of
'Lookback'
Instrument type, specified as a string with the value of
"Lookback"
, a character vector with the value of
'Lookback'
, an
NINST
-by-1
string array with
values "Lookback"
, or an
NINST
-by-1
cell array of
character vectors with values of 'Lookback'
.
Data Types: char
| cell
| string
Specify required
and optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where
Name
is the argument name and Value
is
the corresponding value. Name-value arguments must appear after other arguments,
but the order of the pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: LookbackObj =
fininstrument("Lookback",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"European",'Name',"lookback_option")
Lookback
Name-Value Pair ArgumentsStrike
— Option strike price value
nonnegative numeric | vector of nonnegative values | NaN
Option strike price value, specified as the comma-separated pair
consisting of 'Strike'
and a scalar nonnegative
numeric value or an NINST
-by-1
vector of nonnegative values for a fixed-strike
Lookback
option. For a floating-strike
Lookback
option, specify
'Strike'
as a NaN
or an
NINST
-by-1
vector of
NaN
s.
Note
Use the ConzeViswanathan
pricer for a fixed strike
Lookback
option and use the GoldmanSosinGatto
pricer for a floating strike
Lookback
option.
Data Types: double
ExerciseDate
— Option exercise date
datetime array | string array | date character vector
Option exercise date, specified as the comma-separated pair
consisting of 'ExerciseDate'
and a scalar or an
NINST
-by-1
vector using a
datetime array, string array, or date character vectors.
Note
For a European option, there is only one
ExerciseDate
on the option expiry
date.
To support existing code, Lookback
also
accepts serial date numbers as inputs, but they are not recommended.
If you use date character vectors or strings, the format must be
recognizable by datetime
because
the ExerciseDate
property is stored as a
datetime.
Lookback
Name-Value Pair ArgumentsOptionType
— Option type
"call"
(default) | string with value "call"
or
"put"
| string array with values "call"
or
"put"
| character vector with value 'call'
or
'put'
| cell array of character vectors with values
'call'
or 'put'
Option type, specified as the comma-separated pair consisting of
'OptionType'
and a scalar string or character
vector or an NINST
-by-1
cell
array of character vectors or string array.
A lookback call option gives the holder the right to buy the underlying asset at the highest price observed during the option's term. This allows the holder to benefit from the highest possible purchase price.
A lookback put option provides the holder with the right to sell the underlying asset at the lowest price observed during the option's term. This allows the holder to take advantage of the lowest possible selling price.
Data Types: char
| cell
| string
ExerciseStyle
— Option exercise style
"European"
(default) | string with value "European"
or
"American"
| string array with values "European"
or
"American"
| character vector with value 'European'
or
'American'
| cell array of character vectors with values
'European'
or
'American'
Option exercise style, specified as the comma-separated pair
consisting of 'ExerciseStyle'
and a scalar string
or character vector or an
NINST
-by-1
cell array of
character vectors or string array.
Lookback options can be either European-style or American-style, depending on when they can be exercised:
European Lookback Option — This type of lookback option can only be exercised at the expiration date.
American Lookback Option — An American-style lookback option allows the holder to exercise the option at any time during the option's term.
Data Types: string
| cell
| char
AssetMinMax
— Maximum or minimum underlying asset price
NaN
where
SpotPrice
of the underlying asset is
used (default) | scalar numeric | numeric vector
Maximum or minimum underlying asset price, specified as the
comma-separated pair consisting of 'AssetMinMax'
and a scalar numeric or an
NINST
-by-1
numeric
vector.
Data Types: double
Name
— User-defined name for instrument
" "
(default) | string | string array | character vector | cell array of character vectors
User-defined name for one of more instruments, specified as the
comma-separated pair consisting of 'Name'
and a
scalar string or character vector or an
NINST
-by-1
cell array of
character vectors or string array.
Data Types: char
| cell
| string
Properties
Strike
— Option strike price value
nonnegative numeric | vector of nonnegative values
Option strike price value, returned as a scalar nonnegative numeric or an
NINST
-by-1
vector of nonnegative
values.
Data Types: double
ExerciseDate
— Option exercise date
datetime | vector of datetimes
Option exercise date, returned as a datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
OptionType
— Option type
"call"
(default) | string with value "call"
or
"put"
| string array with values "call"
or
"put"
Option type, returned as a scalar string or an
NINST
-by-1
string array with the
values of "call"
or "put"
.
Data Types: string
ExerciseStyle
— Option exercise style
"European"
(default) | string with value "European"
or
"American"
| string array with values "European"
or
"American"
Option exercise style, returned as a scalar string or an
NINST
-by-1
string array with
values of "European"
or "American"
.
Data Types: string
AssetMinMax
— Maximum or minimum underlying asset price
NaN
where SpotPrice
of the underlying asset is used (default) | scalar numeric | numeric vector
Maximum or minimum underlying asset price, returned as a scalar numeric or
an NINST
-by-1
numeric vector.
Data Types: double
Name
— User-defined name for instrument
" "
(default) | string | string array
User-defined name for the instrument, returned as a string or an
NINST
-by-1
string array.
Data Types: string
Examples
Price Lookback
Instrument Using BlackScholes
Model and ConzeViswanathan
Pricer
This example shows the workflow to price a LookBack
instrument when you use a BlackScholes
model and a ConzeViswanathan
pricing method.
Create Lookback
Instrument Object
Use fininstrument
to create a Lookback
instrument object.
LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")
LookbackOpt = Lookback with properties: OptionType: "put" Strike: 105 AssetMinMax: NaN ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "lookback_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2000 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create ConzeViswanathan
Pricer Object
Use finpricer
to create a ConzeViswanathan
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic","Model",BlackScholesModel,"DiscountCurve",myRC,"SpotPrice",100,"DividendValue",0.25,"DividendType","continuous","PricingMethod","ConzeViswanathan")
outPricer = ConzeViswanathan with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 100 DividendValue: 0.2500 DividendType: "continuous"
Price Lookback
Instrument
Use price
to compute the price and sensitivities for the Lookback
instrument.
[Price, outPR] = price(outPricer,LookbackOpt,["all"])
Price = 57.8786
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ ________ _____ ________ ______ _______ _______
57.879 -0.33404 0 -0.57714 32.587 -5.1863 -350.41
Price Multiple Lookback
Instruments Using BlackScholes
Model and ConzeViswanathan
Pricer
This example shows the workflow to price multiple LookBack
instrument when you use a BlackScholes
model and a ConzeViswanathan
pricing method.
Create Lookback
Instrument Object
Use fininstrument
to create a Lookback
instrument object for three Lookback instruments.
LookbackOpt = fininstrument("Lookback",'Strike',[105 ; 120; 140],'ExerciseDate',datetime([2022,9,15 ; 2022,10,15 ; 2022,11,15]),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")
LookbackOpt=3×1 Lookback array with properties:
OptionType
Strike
AssetMinMax
ExerciseStyle
ExerciseDate
Name
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2000 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create ConzeViswanathan
Pricer Object
Use finpricer
to create a ConzeViswanathan
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic","Model",BlackScholesModel,"DiscountCurve",myRC,"SpotPrice",100,"DividendValue",0.25,"DividendType","continuous","PricingMethod","ConzeViswanathan")
outPricer = ConzeViswanathan with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 100 DividendValue: 0.2500 DividendType: "continuous"
Price Lookback
Instruments
Use price
to compute the prices and sensitivities for the Lookback
instruments.
[Price, outPR] = price(outPricer,LookbackOpt,["all"])
Price = 3×1
57.8786
71.3008
88.9673
outPR=3×1 priceresult array with properties:
Results
PricerData
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ ________ _____ ________ ______ _______ _______
57.879 -0.33404 0 -0.57714 32.587 -5.1863 -350.41
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ ________ __________ ________ ______ _______ _______
71.301 -0.32722 2.8422e-06 -0.45894 31.997 -4.5677 -410.15
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ ________ __________ ________ ______ _______ _______
88.967 -0.32033 1.4211e-06 -0.36005 31.395 -3.7989 -489.96
Price Lookback
Instrument Using BlackScholes
Model and AssetTree
Pricer for LR Binomial Tree
This example shows the workflow to price a LookBack
instrument when you use an BlackScholes
model and an AssetTree
pricing method using a Leisen-Reimer (LR) binomial tree.
Create Lookback
Instrument Object
Use fininstrument
to create a Lookback
instrument object.
LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")
LookbackOpt = Lookback with properties: OptionType: "put" Strike: 105 AssetMinMax: NaN ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "lookback_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2000 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create AssetTree
Pricer Object
Use finpricer
to create an AssetTree
pricer object for a LR equity tree and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
NumPeriods = 15; LRPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',150,'PricingMethod',"LeisenReimer",'Maturity',datetime(2022,9,15),'NumPeriods',NumPeriods)
LRPricer = LRTree with properties: InversionMethod: PP1 Strike: 150 Tree: [1x1 struct] NumPeriods: 15 Model: [1x1 finmodel.BlackScholes] DiscountCurve: [1x1 ratecurve] SpotPrice: 150 DividendType: "continuous" DividendValue: 0 TreeDates: [21-Dec-2018 09:36:00 28-Mar-2019 19:12:00 04-Jul-2019 04:48:00 09-Oct-2019 14:24:00 15-Jan-2020 00:00:00 21-Apr-2020 09:36:00 27-Jul-2020 19:12:00 02-Nov-2020 04:48:00 ... ] (1x15 datetime)
LRPricer.Tree
ans = struct with fields:
Probs: [2x15 double]
ATree: {1x16 cell}
dObs: [15-Sep-2018 00:00:00 21-Dec-2018 09:36:00 28-Mar-2019 19:12:00 04-Jul-2019 04:48:00 09-Oct-2019 14:24:00 15-Jan-2020 00:00:00 21-Apr-2020 09:36:00 27-Jul-2020 19:12:00 02-Nov-2020 04:48:00 ... ] (1x16 datetime)
tObs: [0 0.2667 0.5333 0.8000 1.0667 1.3333 1.6000 1.8667 2.1333 2.4000 2.6667 2.9333 3.2000 3.4667 3.7333 4]
Price Lookback
Instrument
Use price
to compute the price and sensitivities for the Lookback
instrument.
[Price, outPR] = price(LRPricer,LookbackOpt,["all"])
Price = 3.9412
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Vega Lambda Rho Theta
______ ________ _________ ______ _______ _______ _______
3.9412 -0.13312 -0.011131 67.684 -5.0757 -73.857 -1.0383
Price Lookback
Instrument Using BlackScholes
Model and AssetTree
Pricer for Standard Trinomial Tree
This example shows the workflow to price a LookBack
instrument when you use an BlackScholes
model and an AssetTree
pricing method using a Standard Trinomial (STT) tree.
Create Lookback
Instrument Object
Use fininstrument
to create a Lookback
instrument object.
LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")
LookbackOpt = Lookback with properties: OptionType: "put" Strike: 105 AssetMinMax: NaN ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "lookback_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2000 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create AssetTree
Pricer Object
Use finpricer
to create an AssetTree
pricer object for a Standard Trinomial (STT) equity tree and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
NumPeriods = 15; STTPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',150,'PricingMethod',"StandardTrinomial",'Maturity',datetime(2022,9,15),'NumPeriods',NumPeriods)
STTPricer = STTree with properties: Tree: [1x1 struct] NumPeriods: 15 Model: [1x1 finmodel.BlackScholes] DiscountCurve: [1x1 ratecurve] SpotPrice: 150 DividendType: "continuous" DividendValue: 0 TreeDates: [21-Dec-2018 09:36:00 28-Mar-2019 19:12:00 04-Jul-2019 04:48:00 09-Oct-2019 14:24:00 15-Jan-2020 00:00:00 21-Apr-2020 09:36:00 27-Jul-2020 19:12:00 02-Nov-2020 04:48:00 ... ] (1x15 datetime)
STTPricer.Tree
ans = struct with fields:
ATree: {1x16 cell}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double] [3x9 double] [3x11 double] [3x13 double] [3x15 double] [3x17 double] [3x19 double] [3x21 double] [3x23 double] [3x25 double] [3x27 double] [3x29 double]}
dObs: [15-Sep-2018 00:00:00 21-Dec-2018 09:36:00 28-Mar-2019 19:12:00 04-Jul-2019 04:48:00 09-Oct-2019 14:24:00 15-Jan-2020 00:00:00 21-Apr-2020 09:36:00 27-Jul-2020 19:12:00 02-Nov-2020 04:48:00 ... ] (1x16 datetime)
tObs: [0 0.2667 0.5333 0.8000 1.0667 1.3333 1.6000 1.8667 2.1333 2.4000 2.6667 2.9333 3.2000 3.4667 3.7333 4]
Price Lookback
Instrument
Use price
to compute the price and sensitivities for the Lookback
instrument.
[Price, outPR] = price(STTPricer,LookbackOpt,["all"])
Price = 3.3392
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Vega Lambda Rho Theta
______ ________ ___________ ______ _______ _______ _______
3.3392 -0.15942 -1.0596e-11 63.886 -7.1613 -68.263 -1.0254
Price Lookback
Instrument Using BlackScholes
Model and AssetMonteCarlo
Pricer
This example shows the workflow to price a LookBack
instrument when you use a BlackScholes
model and an AssetMonetCarlo
pricing method.
Create Lookback
Instrument Object
Use fininstrument
to create a Lookback
instrument object.
LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")
LookbackOpt = Lookback with properties: OptionType: "put" Strike: 105 AssetMinMax: NaN ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "lookback_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2000 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create AssetMonteCarlo
Pricer Object
Use finpricer
to create an AssetMonteCarlo
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BlackScholesModel,'SpotPrice',200,'simulationDates',datetime(2022,9,15))
outPricer = GBMMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 200 SimulationDates: 15-Sep-2022 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.BlackScholes] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"
Price Lookback
Instrument
Use price
to compute the price and sensitivities for the Lookback
instrument.
[Price, outPR] = price(outPricer,LookbackOpt,["all"])
Price = 1.8553
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Rho Theta Vega
______ _________ __________ _______ _______ ________ ______
1.8553 -0.040442 0.00062792 -4.3596 -39.426 -0.71345 42.311
Price Lookback
Instrument Using BlackScholes
Model and AssetMonteCarlo
Pricer with Quasi-Monte Carlo Simulation
This example shows the workflow to price a LookBack
instrument when you use a BlackScholes
model and an AssetMonetCarlo
pricing method with quasi-Monte Carlo simulation.
Create Lookback
Instrument Object
Use fininstrument
to create a Lookback
instrument object.
LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")
LookbackOpt = Lookback with properties: OptionType: "put" Strike: 105 AssetMinMax: NaN ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "lookback_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.2)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2000 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create AssetMonteCarlo
Pricer Object
Use finpricer
to create an AssetMonteCarlo
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value argument and use the name-value arguments for MonteCarloMethod
and BrownianMotionMethod
.
outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BlackScholesModel,'SpotPrice',200,'simulationDates',datetime(2022,9,15),'NumTrials',1e3, ... 'MonteCarloMethod',"quasi",'BrownianMotionMethod',"brownian-bridge")
outPricer = GBMMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 200 SimulationDates: 15-Sep-2022 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.BlackScholes] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "quasi" BrownianMotionMethod: "brownian-bridge"
Price Lookback
Instrument
Use price
to compute the price and sensitivities for the Lookback
instrument.
[Price, outPR] = price(outPricer,LookbackOpt,"all")
Price = 1.8493
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Rho Theta Vega
______ _________ _________ _______ _______ ________ ______
1.8493 -0.045633 0.0011617 -4.9352 -43.807 -0.79718 47.192
Price Lookback
Instrument Using Bates
Model and AssetMonteCarlo
Pricer
This example shows the workflow to price a LookBack
instrument when you use a Bates
model and an AssetMonetCarlo
pricing method.
Create Lookback
Instrument Object
Use fininstrument
to create a Lookback
instrument object.
LookbackOpt = fininstrument("Lookback",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"lookback_option")
LookbackOpt = Lookback with properties: OptionType: "put" Strike: 105 AssetMinMax: NaN ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "lookback_option"
Create Bates
Model Object
Use finmodel
to create a Bates
model object.
BatesModel = finmodel("Bates",'V0',0.032,'ThetaV',0.1,'Kappa',0.003,'SigmaV',0.2,'RhoSV',0.9,'MeanJ',0.11,'JumpVol',.023,'JumpFreq',0.02)
BatesModel = Bates with properties: V0: 0.0320 ThetaV: 0.1000 Kappa: 0.0030 SigmaV: 0.2000 RhoSV: 0.9000 MeanJ: 0.1100 JumpVol: 0.0230 JumpFreq: 0.0200
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,9,15); Maturity = datetime(2023,9,15); Rate = 0.035; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',12)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 12 Dates: 15-Sep-2023 Rates: 0.0350 Settle: 15-Sep-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create AssetMonteCarlo
Pricer Object
Use finpricer
to create an AssetMonteCarlo
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("AssetMonteCarlo",'DiscountCurve',myRC,"Model",BatesModel,'SpotPrice',100,'simulationDates',datetime(2022,9,15))
outPricer = BatesMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 100 SimulationDates: 15-Sep-2022 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.Bates] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"
Price Lookback
Instrument
Use price
to compute the price and sensitivities for the Lookback
instrument.
[Price, outPR] = price(outPricer,LookbackOpt,["all"])
Price = 7.2577
outPR = priceresult with properties: Results: [1x8 table] PricerData: [1x1 struct]
outPR.Results
ans=1×8 table
Price Delta Gamma Lambda Rho Theta Vega VegaLT
______ ________ _____ _______ _______ _________ ______ _______
7.2577 -0.84025 0 -11.577 -29.025 -0.027666 30.748 0.68416
More About
Lookback Option
A lookback option is a path-dependent option based on the maximum or minimum value the underlying asset achieves during the entire life of the option.
A lookback option's value is derived from an underlying asset, such as a stock, index, or currency pair. The option holder has the right to buy (call option) or sell (put option) the underlying asset at the most favorable price observed during the specified period.
Financial Instruments Toolbox™ software supports two types of lookback options: fixed and floating. Fixed lookback options have a specified strike price, while floating lookback options have a strike price determined by the asset path. For more information, see Lookback Option.
Version History
Introduced in R2020aR2022b: Serial date numbers not recommended
Although Lookback
supports serial date numbers,
datetime
values are recommended instead. The
datetime
data type provides flexible date and time
formats, storage out to nanosecond precision, and properties to account for time
zones and daylight saving time.
To convert serial date numbers or text to datetime
values, use the datetime
function. For example:
t = datetime(738427.656845093,"ConvertFrom","datenum"); y = year(t)
y = 2021
There are no plans to remove support for serial date number inputs.
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