Asian
Description
Create and price an Asian
instrument object for one ore
more Asian instruments using this workflow:
Use
fininstrument
to create anAsian
instrument object for one or more Asian instruments.Use
finmodel
to specify aBlackScholes
,Heston
,Bates
,RoughBergomi
,RoughHeston
, orMerton
model for theAsian
instrument object.Choose a pricing method.
When using a
BlackScholes
model, usefinpricer
to specify aLevy
,KemnaVorst
,AssetTree
, orTurnbullWakeman
pricing method for one or moreAsian
instruments.When using a
BlackScholes
,Heston
,Bates
, orMerton
model, usefinpricer
to specify anAssetMonteCarlo
pricing method for one or moreAsian
instruments.When using a
RoughBergomi
orRoughHeston
model, usefinpricer
to specify aRoughVolMonteCarlo
pricing method for one or moreAsian
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 an
Asian
instrument, see Choose Instruments, Models, and Pricers.
Creation
Syntax
Description
creates an AsianOpt
= fininstrument(InstrumentType
,'Strike
',strike_price,'ExerciseDate
',exercise_date)Asian
instrument object for one or more Asian
instruments by specifying InstrumentType
and sets the
properties for the
required name-value pair arguments Strike
and
ExerciseDate
.
The Asian
instrument supports arithmetic and geometric,
fixed-strike, and floating-strike Asian options.
sets optional properties using
additional name-value pairs in addition to the required arguments in the
previous syntax. For example, AsianOpt
= fininstrument(___,Name,Value
)AsianOpt =
fininstrument("Asian",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"European",'Name',"asian_option")
creates an Asian
put option with an European exercise.
You can specify multiple name-value pair arguments.
Input Arguments
InstrumentType
— Instrument type
string with value "Asian"
| string array with values of "Asian"
| character vector with value 'Asian'
| cell array of character vectors with values of
'Asian'
Instrument type, specified as a string with the value of
"Asian"
, a character vector with the value of
'Asian'
, an
NINST
-by-1
string array with
values of "Asian"
, or an
NINST
-by-1
cell array of
character vectors with values of 'Asian'
.
Data Types: string
| char
| cell
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: AsianOpt =
fininstrument("Asian",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"European",'Name',"asian_option")
Asian
Name-Value Pair ArgumentsStrike
— Option strike price value
nonnegative value | vector of nonnegative values
Option strike price value, specified as the comma-separated pair
consisting of 'Strike'
and a scalar nonnegative
value or an NINST
-by-1
vector
of nonnegative values.
Data Types: double
ExerciseDate
— Option exercise dates
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 an Asian European option, there is only one
ExerciseDate
on the option expiry
date.
To support existing code, Asian
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.
Asian
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 character vector or
string or an NINST
-by-1
cell
array of character vectors or string array.
Data Types: char
| string
| cell
ExerciseStyle
— Option exercise style
"European"
(default) | string with value "European"
| string array with a value "European"
| character vector with value 'European'
| cell array of character vectors with a value
'European'
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.
Data Types: string
| char
| cell
AverageType
— Average type
"arithmetic"
(default) | string with value "arithmetic"
or
"geometric"
| string array with values "arithmetic"
or
"geometric"
| character vector with value 'arithmetic'
or
'geometric'
| cell array of character vectors with values
'arithmetic'
or
'geometric'
Average types, specified as the comma-separated pair consisting of
'AverageType'
and a scalar string or
character vector or an
NINST
-by-1
cell array of
character vectors or string array. Use
"arithmetic"
for an arithmetic average, or
"geometric"
for a geometric average.
Note
When you use a RollGeskeWhaley
pricer, the
AverageType
must be
"geometric"
.
Data Types: char
| cell
| string
AveragePrice
— Average price of underlying asset
0
(default) | scalar numeric | numeric vector
Average price of the underlying asset, specified as the
comma-separated pair consisting of 'AveragePrice'
and a scalar numeric or an
NINST
-by-1
numeric
vector.
Data Types: double
AverageStartDate
— Start date of averaging period
datetime array | string array | date character vector
Start date of averaging period, specified as the comma-separated
pair consisting of 'AverageStartDate'
and a
scalar or an NINST
-by-1
vector
using a datetime array, string array, or date character
vectors.
To support existing code, Asian
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 AverageStartDate
property is stored as a
datetime
.
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 value | vector of nonnegative values
Option strike price value, returned as a scalar nonnegative value 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 scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
OptionType
— Option type
"call"
(default) | scalar 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) | scalar string with value "European"
| string array with values "European"
Option exercise style, returned as a scalar string with the value
"European"
or
NINST
-by-1
string array.
Data Types: string
AverageType
— Average type
"arithmetic"
(default) | scalar string with value "arithmetic"
or
"geometric"
| string array with value "arithmetic"
or
"geometric"
Average types, returned as a scalar string with the value
"arithmetic"
for arithmetic average or
"geometric"
for geometric average or an
NINST
-by-1
string array.
Data Types: string
AveragePrice
— Average price of underlying asset at Settle
0
(default) | scalar numeric | numeric vector
Average price of underlying asset at Settle
, returned
as a scalar numeric or an NINST
-by-1
numeric vector.
Data Types: double
AverageStartDate
— Start date of averaging period
NaT
(default) | datetime | vector of datetimes
Start date of averaging period, returned as a scalar datetime or an
NINST
-by-1
vector of
datetimes.
Data Types: datetime
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 Asian
Instrument Using BlackScholes
Model and TurnbullWakeman
Pricer
This example shows the workflow to price a fixed-strike Asian
instrument when you use a BlackScholes
model and a TurnbullWakeman
pricing method.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "asian_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',.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 TurnbullWakeman
Pricer Object
Use finpricer
to create a TurnbullWakeman
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',1000,'PricingMethod',"TurnbullWakeman")
outPricer = TurnbullWakeman with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 1000 DividendValue: 0 DividendType: "continuous"
Price Asian
Instrument
Use price
to compute the price and sensitivities for the Asian
instrument.
[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 56.7068
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ _______ _________ _______ ______ _______ _______
56.707 -0.3155 0.0014381 -5.5637 408.85 -2.9341 -832.53
Price Multiple Asian
Instruments Using BlackScholes
Model and TurnbullWakeman
Pricer
This example shows the workflow to price multiple fixed-strike Asian
instruments when you use a BlackScholes
model and a TurnbullWakeman
pricing method.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object for three Asian instruments.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime([2022,9,15; 2022,10,15; 2022,11,15]),'Strike',[1000 ; 2000 ; 3000],'OptionType',"put",'Name',"asian_option")
AsianOpt=3×1 Asian array with properties:
OptionType
Strike
AverageType
AveragePrice
AverageStartDate
ExerciseStyle
ExerciseDate
Name
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',.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 TurnbullWakeman
Pricer Object
Use finpricer
to create a TurnbullWakeman
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',1000,'PricingMethod',"TurnbullWakeman")
outPricer = TurnbullWakeman with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 1000 DividendValue: 0 DividendType: "continuous"
Price Asian
Instruments
Use price
to compute the prices and sensitivities for the Asian
instruments.
[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 3×1
103 ×
0.0567
0.8023
1.6624
outPR=3×1 priceresult array with properties:
Results
PricerData
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ _______ _________ _______ ______ _______ _______
56.707 -0.3155 0.0014381 -5.5637 408.85 -2.9341 -832.53
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ ________ __________ _______ ______ ______ _______
802.32 -0.92568 7.9581e-05 -1.1537 20.935 44.139 -5206.3
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ ________ __________ ________ ________ ______ _______
1662.4 -0.93048 4.5475e-05 -0.55973 0.093861 74.863 -8911.1
Price Asian
Instrument Using BlackScholes
Model and AssetTree
Pricer for CRR Binomial Tree
This example shows the workflow to price a fixed-strike Asian
instrument when you use a BlackScholes
model and an AssetTree
pricing method for a Cox-Ross-Rubinstein (CRR) binomial tree.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "asian_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 CRR equity tree and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
NumPeriods = 15; CRRPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',1000,'PricingMethod',"CoxRossRubinstein",'Maturity',datetime(2022,9,15),'NumPeriods',NumPeriods)
CRRPricer = CRRTree with properties: Tree: [1x1 struct] NumPeriods: 15 Model: [1x1 finmodel.BlackScholes] DiscountCurve: [1x1 ratecurve] SpotPrice: 1000 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)
CRRPricer.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 Asian
Instrument
Use price
to compute the price and sensitivities for the Asian
instrument.
[Price, outPR] = price(CRRPricer,AsianOpt,["all"])
Price = 54.9225
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Vega Lambda Rho Theta
______ ________ ______ ______ _______ _______ _______
54.922 -0.32119 0.0581 393.85 -5.8481 -846.57 -2.4325
Price Asian
Instrument Using BlackScholes
Model and AssetTree
Pricer for Standard Trinomial Tree
This example shows the workflow to price a fixed-strike Asian
instrument when you use a BlackScholes
model and an AssetTree
pricing method for a Standard Trinomial (STT) tree.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "asian_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 tree and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
NumPeriods = 15; STTPricer = finpricer("AssetTree",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',1000,'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: 1000 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 Asian
Instrument
Use price
to compute the price and sensitivities for the Asian
instrument.
[Price, outPR] = price(STTPricer,AsianOpt,["all"])
Price = 54.2450
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Vega Lambda Rho Theta
______ ________ ________ ______ _______ _______ _______
54.245 -0.32307 0.075269 390.55 -5.9558 -839.02 -2.4161
Price Asian
Instrument for Foreign Exchange Using BlackScholes
Model and Levy
Pricer
This example shows the workflow to price an Asian
instrument for an arithmetic average currency option when you use a BlackScholes
model and a Levy
pricing method. Assume that the current exchange rate is $0.52 and has a volatility of 12% per annum. The annualized continuously compounded foreign risk-free rate is 8% per annum.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',0.65,'OptionType',"put",'ExerciseStyle',"european",'Name',"asian_fx_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 0.6500 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "asian_fx_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
Sigma = .12; BlackScholesModel = finmodel("BlackScholes",'Volatility',Sigma)
BlackScholesModel = BlackScholes with properties: Volatility: 0.1200 Correlation: 1
Create ratecurve
Object
Create a 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 Levy
Pricer Object
Use finpricer
to create a Levy
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument. When you price currencies using an Asian instrument for an arithmetic average currency option, the DividendType
must be 'continuous'
and DividendValue
is the annualized risk-free interest rate in the foreign country.
ForeignRate = 0.08; outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',.52,'DividendType',"continuous",'DividendValue',ForeignRate,'PricingMethod',"Levy")
outPricer = Levy with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 0.5200 DividendValue: 0.0800 DividendType: "continuous"
Price Asian
FX Instrument
Use price
to compute the price and sensitivities for the Asian
FX instrument.
[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 0.1516
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
_______ ________ _______ _______ ________ __________ _______
0.15161 -0.78532 0.37534 -2.6935 0.015668 -0.0038317 -1.3974
Price Asian
Instrument Using BlackScholes
Model and AssetMonteCarlo
Pricer
This example shows the workflow to price a fixed-strike Asian
instrument when you use a BlackScholes
model and an AssetMonteCarlo
pricing method.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "asian_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 Asian
Instrument
Use price
to compute the price and sensitivities for the Asian
instrument.
[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 682.3365
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Rho Theta Vega
______ ________ ___________ ________ _______ ______ _______
682.34 -0.93511 -5.6843e-14 -0.27409 -3129.1 27.433 -1.2121
Price Asian
Instrument Using Merton
Model and AssetMonteCarlo
Pricer
This example shows the workflow to price a fixed-strike Asian
instrument when you use a Merton
model and an AssetMonteCarlo
pricing method.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2022,9,15),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Name: "asian_option"
Create Merton
Model Object
Use finmodel
to create a Merton
model object.
MertonModel = finmodel("Merton",'Volatility',0.45,'MeanJ',0.02,'JumpVol',0.07,'JumpFreq',0.09)
MertonModel = Merton with properties: Volatility: 0.4500 MeanJ: 0.0200 JumpVol: 0.0700 JumpFreq: 0.0900
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",MertonModel,'SpotPrice',200,'simulationDates',datetime(2022,9,15))
outPricer = MertonMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 200 SimulationDates: 15-Sep-2022 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.Merton] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"
Price Asian
Instrument
Use price
to compute the price and sensitivities for the Asian
instrument.
[Price, outPR] = price(outPricer,AsianOpt,["all"])
Price = 682.8127
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Rho Theta Vega
______ ________ _____ ________ _______ _____ ______
682.81 -0.90665 0 -0.26556 -3110.3 25.98 19.316
Price Asian
Instrument Using RoughBergomi
Model and RoughVolMonteCarlo
Pricer
Since R2024a
This example shows the workflow to price a fixed-strike Asian
instrument when you use a RoughBergomi
model and an RoughVolMonteCarlo
pricing method.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",'ExerciseDate',datetime(2019,1,30),'Strike',1000,'OptionType',"put",'Name',"asian_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 30-Jan-2019 Name: "asian_option"
Create RoughBergomi
Model Object
Use finmodel
to create a RoughBergomi
model object.
RoughBergomiModel = finmodel("RoughBergomi",Alpha=-0.32, Xi=0.1,Eta=0.003,RhoSV=0.9)
RoughBergomiModel = RoughBergomi with properties: Alpha: -0.3200 Xi: 0.1000 Eta: 0.0030 RhoSV: 0.9000
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 RoughVolMonteCarlo
Pricer Object
Use finpricer
to create an RoughVolMonteCarlo
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value argument.
outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughBergomiModel,SpotPrice=900,simulationDates=datetime(2019,1,30))
outPricer = RoughBergomiMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 900 SimulationDates: 30-Jan-2019 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.RoughBergomi] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"
Price Asian
Instrument
Use price
to compute the price and sensitivities for the Asian
instrument.
[Price, outPR] = price(outPricer,AsianOpt,"all")
Price = 103.0639
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Rho Theta Vega
______ ________ _________ _______ _______ _______ ______
103.06 -0.77793 0.0024128 -6.7932 -166.05 -1.4838 88.272
Price Asian
Instrument Using RoughHeston
Model and RoughVolMonteCarlo
Pricer
Since R2024b
This example shows the workflow to price a fixed-strike Asian
instrument when you use a RoughHeston
model and a RoughVolMonteCarlo
pricing method.
Create Asian
Instrument Object
Use fininstrument
to create an Asian
instrument object.
AsianOpt = fininstrument("Asian",ExerciseDate=datetime(2019,1,30),Strike=1000,OptionType="put",Name="asian_option")
AsianOpt = Asian with properties: OptionType: "put" Strike: 1000 AverageType: "arithmetic" AveragePrice: 0 AverageStartDate: NaT ExerciseStyle: "european" ExerciseDate: 30-Jan-2019 Name: "asian_option"
Create RoughHeston
Model Object
Use finmodel
to create a RoughHeston
model object.
RoughHestonModel = finmodel("RoughHeston",V0=0.4,ThetaV=0.3,Kappa=0.2,SigmaV=0.1,Alpha=-0.02,RhoSV=0.3)
RoughHestonModel = RoughHeston with properties: Alpha: -0.0200 V0: 0.4000 ThetaV: 0.3000 Kappa: 0.2000 SigmaV: 0.1000 RhoSV: 0.3000
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 RoughVolMonteCarlo
Pricer Object
Use finpricer
to create a RoughVolMonteCarlo
pricer object and use the ratecurve
object for the DiscountCurve
name-value argument.
outPricer = finpricer("RoughVolMonteCarlo",DiscountCurve=myRC,Model=RoughHestonModel,SpotPrice=900,simulationDates=datetime(2019,1,30))
outPricer = RoughHestonMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 900 SimulationDates: 30-Jan-2019 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.RoughHeston] DividendType: "continuous" DividendValue: 0 MonteCarloMethod: "standard" BrownianMotionMethod: "standard"
Price Asian
Instrument
Use price
to compute the price and sensitivities for the Asian
instrument.
[Price, outPR] = price(outPricer,AsianOpt,"all")
Price = 131.2194
outPR = priceresult with properties: Results: [1x8 table] PricerData: [1x1 struct]
outPR.Results
ans=1×8 table
Price Delta Gamma Lambda Rho Theta Vega VegaLT
______ ________ _______ _______ ______ _______ ______ ______
131.22 -0.67246 0.00155 -4.6122 -152.4 -74.841 105.65 0
More About
Asian Option
An Asian option is a path-dependent option with a payoff linked to the average value of the underlying asset during the life (or some part of the life) of the option.
The payoff of an Asian option depends on the average price of the underlying asset over a specific period, known as the averaging period. The averaging can be done using various methods, such as arithmetic mean or geometric mean. The payoff of an Asian option is determined by comparing the average price of the underlying asset during the averaging period to the strike price. If the average price is favorable, the option holder receives a positive payoff.
Asian options are similar to lookback options in that there are two types of Asian options: fixed (average price option) and floating (average strike option). Fixed Asian options have a specified strike, while floating Asian options have a strike equal to the average value of the underlying asset over the life of the option. For more information, see Asian Option.
Version History
Introduced in R2020aR2024b: Support for RoughHeston
model and RoughVolMonteCarlo
pricer
The Asian
instrument object supports pricing with a RoughHeston
model and
a RoughVolMonteCarlo
pricing method.
R2024a: Support for RoughBergomi
model and RoughVolMonteCarlo
pricer
The Asian
instrument object supports pricing with a RoughBergomi
model
and a RoughVolMonteCarlo
pricing method.
R2022b: Serial date numbers not recommended
Although Asian
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.
MATLAB 명령
다음 MATLAB 명령에 해당하는 링크를 클릭했습니다.
명령을 실행하려면 MATLAB 명령 창에 입력하십시오. 웹 브라우저는 MATLAB 명령을 지원하지 않습니다.
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