Vanilla
Description
Create and price a Vanilla
instrument object for one or
more Vanilla instruments using this workflow:
Use
fininstrument
to create aVanilla
instrument object for one or more Vanilla instruments.Use
finmodel
to specify aBlackScholes
,Bachelier
,Heston
,Bates
,Merton
, orDupire
model for theVanilla
instrument object.Choose a pricing method.
When using a
BlackScholes
model, usefinpricer
to specify aFiniteDifference
,BlackScholes
,BjerksundStensland
,RollGeskeWhaley
,VannaVolga
,AssetTree
, orAssetMonteCarlo
pricing method for one or moreVanilla
instruments.When using a
Heston
,Bates
, orMerton
model, usefinpricer
to specify aFiniteDifference
,NumericalIntegration
,FFT
, orAssetMonteCarlo
pricing method for one or moreVanilla
instruments.When using a
Dupire
model, usefinpricer
to specify aFiniteDifference
pricing method for one or moreVanilla
instruments.When using a
Bachelier
model, usefinpricer
to specify anAssetMonteCarlo
pricing method for one or moreVanilla
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
Vanilla
instrument, see Choose Instruments, Models, and Pricers.
Creation
Syntax
Description
creates a VanillaObj
= fininstrument(InstrumentType
,'Strike
',strike_value,'ExerciseDate
',exercise_date)Vanilla
object for one or more Vanilla
instruments by specifying InstrumentType
and sets the
properties for the
required name-value pair arguments Strike
and
ExerciseDate
. For more information on a
Vanilla
instrument, see More About.
sets optional properties using
additional name-value pairs in addition to the required arguments in the
previous syntax. For example, VanillaObj
= fininstrument(___,Name,Value
)VanillaObj =
fininstrument("Vanilla",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"American",'Name',"vanilla_instrument")
creates a Vanilla
put option with an American exercise.
You can specify multiple name-value pair arguments.
Input Arguments
InstrumentType
— Instrument type
string with value "Vanilla"
| string array with values of "Vanilla"
| character vector with value 'Vanilla'
| cell array of character vectors with values of
'Vanilla'
Instrument type, specified as a string with the value of
"Vanilla"
, a character vector with the value of
'Vanilla'
, an
NINST
-by-1
string array with
values of "Vanilla"
, or an
NINST
-by-1
cell array of
character vectors with values of 'Vanilla'
.
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: VanillaObj =
fininstrument("Vanilla",'Strike',100,'ExerciseDate',datetime(2019,1,30),'OptionType',"put",'ExerciseStyle',"American",'Name',"vanilla_instrument")
Vanilla
Name-Value Pair ArgumentsStrike
— Option strike price value
nonnegative numeric | nonnegative numeric vector
Option strike price value, specified as the comma-separated pair
consisting of 'Strike'
and a scalar nonnegative
numeric value or an NINST
-by-1
nonnegative numeric vector.
Note
When using a "Bermudan"
ExerciseStyle
with a FiniteDifference
pricer, the
Strike
is a vector.
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.
When using a "Bermudan"
ExerciseStyle
with a FiniteDifference
pricer, the
ExerciseDate
is a vector.
To support existing code, Vanilla
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.
Vanilla
Name-Value Pair ArgumentsOptionType
— Option type
"call"
(default) | string with value "call"
or
"put"
| string array with values of "call"
or
"put"
| character vector with value 'call'
or
'put'
| cell array of character vectors with values of
'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.
Note
When you use a RollGeskeWhaley
pricer with a
Vanilla
option,
OptionType
must be
'call'
.
Data Types: char
| cell
| string
ExerciseStyle
— Option exercise style
"European"
(default) | string with value "European"
,
"American"
, or "Bermudan"
| string array with values of "European"
,
"American"
, or "Bermudan"
| character vector with value 'European'
,
'American'
, or
'Bermudan'
| cell array of character vectors with values of
'European'
, 'American'
, or
'Bermudan'
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.
Note
When you use a
BlackScholes
pricer with aVanilla
option, the'American'
option type is not supported.When you use a
RollGeskeWhaley
or aBjerksundStensland
pricer with aVanilla
option, you must specify an'American'
option.When you use a
NumericalIntegration
pricer with aBates
,Merton
, orHeston
model for aVanilla
option, theExerciseStyle
must be'European'
.When you use a
FFT
pricer with aBates
,Merton
, orHeston
model for aVanilla
option, theExerciseStyle
must be'European'
.When you use an
AssetMonteCarlo
pricer with aBlackScholes
,Bates
,Merton
, orHeston
model for aVanilla
option, theExerciseStyle
can be'American'
,'European'
, or'Bermudan'
.When you use a
FiniteDifference
pricer with aBlackScholes
,Bachelier
,Dupire
,Bates
,Merton
, orHeston
model for aVanilla
option, theExerciseStyle
can be'American'
,'European'
, or'Bermudan'
.
For more information on
ExerciseStyle
, see Supported Exercise Styles.
Data Types: string
| cell
| char
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 | nonnegative numeric vector
Option strike price value, returned as a scalar nonnegative numeric or an
NINST
-by-1
nonnegative numeric
vector.
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) | string with value "call"
or
"put"
| string array with values of "call"
or
"put"
Option type, returned as a scalar string or an
NINST
-by-1
string array with
values of "call"
or "put"
.
Data Types: string
ExerciseStyle
— Option type
"European"
(default) | string with value "European"
,
"American"
, or "Bermudan"
| string array with values of "European"
,
"American"
, or "Bermudan"
Option exercise style, returned as a scalar string or an
NINST
-by-1
string array with
values of "European"
, "American"
, or
"Bermudan"
.
Data Types: string
Name
— User-defined name for instrument
" "
(default) | string | string array
User-defined name for the instrument, returned as a scalar string or an
NINST
-by-1
string array.
Data Types: string
Object Functions
setExercisePolicy | Set exercise policy for FixedBondOption ,
FloatBondOption , or Vanilla instrument |
Examples
Price Vanilla Instrument Using Black-Scholes Model and Black-Scholes Pricer
This example shows the workflow to price a Vanilla
instrument when you use a BlackScholes
model and a BlackScholes
pricing method.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2018,5,1),'Strike',29,'OptionType',"put",'ExerciseStyle',"european",'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "put" ExerciseStyle: "european" ExerciseDate: 01-May-2018 Strike: 29 Name: "vanilla_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.25)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2500 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1); Maturity = datetime(2019,1,1); Rate = 0.05; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 1 Dates: 01-Jan-2019 Rates: 0.0500 Settle: 01-Jan-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create BlackScholes
Pricer Object
Use finpricer
to create a BlackScholes
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',30,'DividendValue',0.045)
outPricer = BlackScholes with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 30 DividendValue: 0.0450 DividendType: "continuous"
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 1.2046
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
______ ________ ________ _______ ______ _______ _______
1.2046 -0.36943 0.086269 -9.3396 6.4702 -4.0959 -2.3107
Price Multiple Vanilla Instruments Using Black-Scholes Model and Black-Scholes Pricer
This example shows the workflow to price multiple Vanilla
instrument when you use a BlackScholes
model and a BlackScholes
pricing method.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object for three Vanilla instruments.
VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime([2018,5,1 ; 2018,6,1 ; 2018,7,1]),'Strike',[29 ; 38 ; 70],'OptionType',"put",'ExerciseStyle',"european",'Name',"vanilla_option")
VanillaOpt=3×1 object
3x1 Vanilla array with properties:
OptionType
ExerciseStyle
ExerciseDate
Strike
Name
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.25)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2500 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1); Maturity = datetime(2019,1,1); Rate = 0.05; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 1 Dates: 01-Jan-2019 Rates: 0.0500 Settle: 01-Jan-2018 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create BlackScholes
Pricer Object
Use finpricer
to create a BlackScholes
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'DiscountCurve',myRC,'Model',BlackScholesModel,'SpotPrice',30,'DividendValue',0.045)
outPricer = BlackScholes with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 30 DividendValue: 0.0450 DividendType: "continuous"
Price Vanilla
Instruments
Use price
to compute the prices and sensitivities for the Vanilla
instruments.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 3×1
1.2046
7.9479
38.9392
outPR=3×1 object
3x1 priceresult array with properties:
Results
PricerData
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
______ ________ ________ _______ ______ _______ _______
1.2046 -0.36943 0.086269 -9.3396 6.4702 -4.0959 -2.3107
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
______ ________ ________ _______ ______ _______ _______
7.9479 -0.89786 0.031587 -3.4532 2.9612 -14.535 -0.3563
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
______ ________ __________ ________ __________ _______ ______
38.939 -0.97775 1.2279e-06 -0.77043 0.00013814 -34.136 2.0936
Price Vanilla Instrument Using Black-Scholes Model and Asset Tree Pricer for LR Binomial Tree
This example shows the workflow to price a Vanilla
instrument when you use a BlackScholes
model and an AssetTree
pricing method using a Leisen-Reimer (LR) binomial tree.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2018,5,1),'Strike',29,'OptionType',"put",'ExerciseStyle',"european",'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "put" ExerciseStyle: "european" ExerciseDate: 01-May-2018 Strike: 29 Name: "vanilla_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.25)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2500 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1); Maturity = datetime(2019,1,1); Rate = 0.05; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 1 Dates: 01-Jan-2019 Rates: 0.0500 Settle: 01-Jan-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',50,'PricingMethod',"LeisenReimer",'Maturity',datetime(2018,5,1),'NumPeriods',NumPeriods)
LRPricer = LRTree with properties: InversionMethod: PP1 Strike: 50 Tree: [1x1 struct] NumPeriods: 15 Model: [1x1 finmodel.BlackScholes] DiscountCurve: [1x1 ratecurve] SpotPrice: 50 DividendType: "continuous" DividendValue: 0 TreeDates: [09-Jan-2018 17-Jan-2018 25-Jan-2018 02-Feb-2018 10-Feb-2018 18-Feb-2018 26-Feb-2018 06-Mar-2018 14-Mar-2018 22-Mar-2018 30-Mar-2018 07-Apr-2018 15-Apr-2018 23-Apr-2018 01-May-2018]
LRPricer.Tree
ans = struct with fields:
Probs: [2x15 double]
ATree: {1x16 cell}
dObs: [01-Jan-2018 09-Jan-2018 17-Jan-2018 25-Jan-2018 02-Feb-2018 10-Feb-2018 18-Feb-2018 26-Feb-2018 06-Mar-2018 14-Mar-2018 22-Mar-2018 30-Mar-2018 07-Apr-2018 15-Apr-2018 23-Apr-2018 01-May-2018]
tObs: [0 0.0222 0.0444 0.0667 0.0889 0.1111 0.1333 0.1556 0.1778 0.2000 0.2222 0.2444 0.2667 0.2889 0.3111 0.3333]
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(LRPricer,VanillaOpt,["all"])
Price = 3.5022e-06
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Vega Lambda Rho Theta
__________ ___________ __________ _________ _______ ___________ ___________
3.5022e-06 -1.9331e-06 1.1068e-06 0.0016243 -30.496 -3.6747e-05 -0.00060106
outPR.PricerData.PriceTree
ans = struct with fields:
PTree: {1x16 cell}
ExTree: {1x16 cell}
tObs: [0 0.0222 0.0444 0.0667 0.0889 0.1111 0.1333 0.1556 0.1778 0.2000 0.2222 0.2444 0.2667 0.2889 0.3111 0.3333]
dObs: [01-Jan-2018 09-Jan-2018 17-Jan-2018 25-Jan-2018 02-Feb-2018 10-Feb-2018 18-Feb-2018 26-Feb-2018 06-Mar-2018 14-Mar-2018 22-Mar-2018 30-Mar-2018 07-Apr-2018 15-Apr-2018 23-Apr-2018 01-May-2018]
Probs: [2x15 double]
outPR.PricerData.PriceTree.ExTree
ans=1×16 cell array
{[0]} {[0 0]} {[0 0 0]} {[0 0 0 0]} {[0 0 0 0 0]} {[0 0 0 0 0 0]} {[0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1]}
Price Vanilla Instrument Using Black-Scholes Model and Asset Tree Pricer for Standard Trinomial Tree
This example shows the workflow to price a Vanilla
instrument when you use a BlackScholes
model and an AssetTree
pricing method using a Standard Trinomial (STT) tree.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2018,5,1),'Strike',29,'OptionType',"put",'ExerciseStyle',"european",'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "put" ExerciseStyle: "european" ExerciseDate: 01-May-2018 Strike: 29 Name: "vanilla_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',0.25)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2500 Correlation: 1
Create ratecurve
Object
Create a flat ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1); Maturity = datetime(2019,1,1); Rate = 0.05; myRC = ratecurve('zero',Settle,Maturity,Rate,'Basis',1)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 1 Dates: 01-Jan-2019 Rates: 0.0500 Settle: 01-Jan-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',50,'PricingMethod',"StandardTrinomial",'Maturity',datetime(2018,5,1),'NumPeriods',NumPeriods)
STTPricer = STTree with properties: Tree: [1x1 struct] NumPeriods: 15 Model: [1x1 finmodel.BlackScholes] DiscountCurve: [1x1 ratecurve] SpotPrice: 50 DividendType: "continuous" DividendValue: 0 TreeDates: [09-Jan-2018 17-Jan-2018 25-Jan-2018 02-Feb-2018 10-Feb-2018 18-Feb-2018 26-Feb-2018 06-Mar-2018 14-Mar-2018 22-Mar-2018 30-Mar-2018 07-Apr-2018 15-Apr-2018 23-Apr-2018 01-May-2018]
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: [01-Jan-2018 09-Jan-2018 17-Jan-2018 25-Jan-2018 02-Feb-2018 10-Feb-2018 18-Feb-2018 26-Feb-2018 06-Mar-2018 14-Mar-2018 22-Mar-2018 30-Mar-2018 07-Apr-2018 15-Apr-2018 23-Apr-2018 01-May-2018]
tObs: [0 0.0222 0.0444 0.0667 0.0889 0.1111 0.1333 0.1556 0.1778 0.2000 0.2222 0.2444 0.2667 0.2889 0.3111 0.3333]
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(STTPricer,VanillaOpt,["all"])
Price = 6.3773e-05
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Vega Lambda Rho Theta
__________ ___________ __________ _________ _______ ___________ _________
6.3773e-05 -9.1432e-06 1.2388e-06 0.0034421 -21.514 -0.00064994 -0.001188
outPR.PricerData.PriceTree
ans = struct with fields:
PTree: {1x16 cell}
ExTree: {1x16 cell}
tObs: [0 0.0222 0.0444 0.0667 0.0889 0.1111 0.1333 0.1556 0.1778 0.2000 0.2222 0.2444 0.2667 0.2889 0.3111 0.3333]
dObs: [01-Jan-2018 09-Jan-2018 17-Jan-2018 25-Jan-2018 02-Feb-2018 10-Feb-2018 18-Feb-2018 26-Feb-2018 06-Mar-2018 14-Mar-2018 22-Mar-2018 30-Mar-2018 07-Apr-2018 15-Apr-2018 23-Apr-2018 01-May-2018]
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]}
outPR.PricerData.PriceTree.ExTree
ans=1×16 cell array
{[0]} {[0 0 0]} {[0 0 0 0 0]} {[0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]} {[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1]}
Price American Option for Vanilla Instrument Using Black-Scholes Model and Roll-Geske-Whaley Pricer
This example shows the workflow to price an American option for a Vanilla
instrument when you use a BlackScholes
model and a RollGeskeWhaley
pricing method.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"call",'ExerciseStyle',"american",'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "american" ExerciseDate: 15-Sep-2022 Strike: 105 Name: "vanilla_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 RollGeskeWhaley
Pricer Object
Use finpricer
to create a RollGeskeWhaley
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',100,'DividendValue',timetable(datetime(2021,6,15),0.25),'PricingMethod',"RollGeskeWhaley")
outPricer = RollGeskeWhaley with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 100 DividendValue: [1x1 timetable] DividendType: "cash"
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 19.9066
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ _______ _________ ______ ______ _______ ______
19.907 0.66568 0.0090971 3.344 72.804 -3.4537 186.68
Price a Vanilla Instrument for Foreign Exchange Using Black-Scholes Model and Black-Scholes Pricer
This example shows the workflow to price a Vanilla
instrument for foreign exchange (FX) when you use a BlackScholes
model and a BlackScholes
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 Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2022,9,15),'Strike',.50,'OptionType',"put",'ExerciseStyle',"european",'Name',"vanilla_fx_option")
VanillaOpt = Vanilla with properties: OptionType: "put" ExerciseStyle: "european" ExerciseDate: 15-Sep-2022 Strike: 0.5000 Name: "vanilla_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 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 BlackScholes
Pricer Object
Use finpricer
to create a BlackScholes
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument. When pricing currencies using a Vanilla
instrument, 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)
outPricer = BlackScholes with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 0.5200 DividendValue: 0.0800 DividendType: "continuous"
Price Vanilla
FX Instrument
Use price
to compute the price and sensitivities for the Vanilla
FX instrument.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 0.0738
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
________ ________ ______ _______ _______ _______ _________
0.073778 -0.49349 2.0818 -4.7899 0.27021 -1.3216 -0.013019
Price American Option for Vanilla Instrument Using Black-Scholes Model and Asset Monte-Carlo Pricer
This example shows the workflow to price an American option for a Vanilla
instrument when you use a BlackScholes
model and an AssetMonteCarlo
pricing method.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"call",'ExerciseStyle',"american",'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "american" ExerciseDate: 15-Sep-2022 Strike: 105 Name: "vanilla_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',150,'simulationDates',datetime(2022,9,15))
outPricer = GBMMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 150 SimulationDates: 15-Sep-2022 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.BlackScholes] DividendType: "continuous" DividendValue: 0
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 61.2010
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Rho Theta Vega
______ _______ _________ ______ ______ _______ ______
61.201 0.93074 0.0027813 2.2812 313.95 -3.7909 41.626
Price American Option for Vanilla Instrument Using Heston Model and Asset Monte-Carlo Pricer
This example shows the workflow to price an American option for a Vanilla
instrument when you use a Heston
model and an AssetMonteCarlo
pricing method.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'Strike',105,'ExerciseDate',datetime(2022,9,15),'OptionType',"call",'ExerciseStyle',"american",'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "american" ExerciseDate: 15-Sep-2022 Strike: 105 Name: "vanilla_option"
Create Heston
Model Object
Use finmodel
to create a Heston
model object.
HestonModel = finmodel("Heston",'V0',0.032,'ThetaV',0.07,'Kappa',0.003,'SigmaV',0.02,'RhoSV',0.09)
HestonModel = Heston with properties: V0: 0.0320 ThetaV: 0.0700 Kappa: 0.0030 SigmaV: 0.0200 RhoSV: 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",HestonModel,'SpotPrice',150,'simulationDates',datetime(2022,9,15))
outPricer = HestonMonteCarlo with properties: DiscountCurve: [1x1 ratecurve] SpotPrice: 150 SimulationDates: 15-Sep-2022 NumTrials: 1000 RandomNumbers: [] Model: [1x1 finmodel.Heston] DividendType: "continuous" DividendValue: 0
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 60.5637
outPR = priceresult with properties: Results: [1x8 table] PricerData: [1x1 struct]
outPR.Results
ans=1×8 table
Price Delta Gamma Lambda Rho Theta Vega VegaLT
______ _______ _________ ______ ______ _______ ______ _______
60.564 0.94774 0.0011954 2.3473 326.36 -3.7126 35.272 0.31155
Price Bermudan Option for Vanilla Instrument Using Black-Scholes Model and Finite Difference Pricer
This example shows the workflow to price a Bermudan option for a Vanilla
instrument when you use a BlackScholes
model and a FiniteDifference
pricing method.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
VanillaOpt = fininstrument("Vanilla",'Strike',[110,120],'ExerciseDate',[datetime(2022,9,15) , datetime(2023,9,15)],'OptionType',"call",'ExerciseStyle',"Bermudan",'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "bermudan" ExerciseDate: [15-Sep-2022 15-Sep-2023] Strike: [110 120] Name: "vanilla_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 FiniteDifference
Pricer Object
Use finpricer
to create a FiniteDifference
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("FiniteDifference",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',100)
outPricer = FiniteDifference with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 100 GridProperties: [1x1 struct] DividendType: "continuous" DividendValue: 0
Price Vanilla
Instrument
Use price
to compute the price and sensitivities for the Vanilla
instrument.
[Price, outPR] = price(outPricer,VanillaOpt,["all"])
Price = 18.6797
outPR = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Theta Rho Vega
_____ _______ _________ ______ _______ ______ ______
18.68 0.62163 0.0091406 3.3278 -3.3154 184.31 83.162
Price Vanilla Instrument Using Heston Model and Multiple Different Pricers
This example shows the workflow to price a Vanilla
instrument when you use a Heston
model and various pricing methods.
Create Vanilla
Instrument Object
Use fininstrument
to create a Vanilla
instrument object.
Settle = datetime(2017,6,29); Maturity = datemnth(Settle,6); Strike = 80; VanillaOpt = fininstrument('Vanilla','ExerciseDate',Maturity,'Strike',Strike,'Name',"vanilla_option")
VanillaOpt = Vanilla with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 29-Dec-2017 Strike: 80 Name: "vanilla_option"
Create Heston
Model Object
Use finmodel
to create a Heston
model object.
V0 = 0.04; ThetaV = 0.05; Kappa = 1.0; SigmaV = 0.2; RhoSV = -0.7; HestonModel = finmodel("Heston",'V0',V0,'ThetaV',ThetaV,'Kappa',Kappa,'SigmaV',SigmaV,'RhoSV',RhoSV)
HestonModel = Heston with properties: V0: 0.0400 ThetaV: 0.0500 Kappa: 1 SigmaV: 0.2000 RhoSV: -0.7000
Create ratecurve
object
Create a ratecurve
object using ratecurve
.
Rate = 0.03;
ZeroCurve = ratecurve('zero',Settle,Maturity,Rate);
Create NumericalIntegration
, FFT
, and FiniteDifference
Pricer Objects
Use finpricer
to create a NumericalIntegration
, FFT
, and FiniteDifference
pricer objects and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
SpotPrice = 80; Strike = 80; DividendYield = 0.02; NIPricer = finpricer("NumericalIntegration",'Model', HestonModel,'SpotPrice',SpotPrice,'DiscountCurve',ZeroCurve,'DividendValue',DividendYield)
NIPricer = NumericalIntegration with properties: Model: [1x1 finmodel.Heston] DiscountCurve: [1x1 ratecurve] SpotPrice: 80 DividendType: "continuous" DividendValue: 0.0200 AbsTol: 1.0000e-10 RelTol: 1.0000e-10 IntegrationRange: [1.0000e-09 Inf] CharacteristicFcn: @characteristicFcnHeston Framework: "heston1993" VolRiskPremium: 0 LittleTrap: 1
FFTPricer = finpricer("FFT",'Model',HestonModel, ... 'SpotPrice',SpotPrice,'DiscountCurve',ZeroCurve, ... 'DividendValue',DividendYield,'NumFFT',8192)
FFTPricer = FFT with properties: Model: [1x1 finmodel.Heston] DiscountCurve: [1x1 ratecurve] SpotPrice: 80 DividendType: "continuous" DividendValue: 0.0200 NumFFT: 8192 CharacteristicFcnStep: 0.0100 LogStrikeStep: 0.0767 CharacteristicFcn: @characteristicFcnHeston DampingFactor: 1.5000 Quadrature: "simpson" VolRiskPremium: 0 LittleTrap: 1
FDPricer = finpricer("FiniteDifference",'Model',HestonModel,'SpotPrice',SpotPrice,'DiscountCurve',ZeroCurve,'DividendValue',DividendYield)
FDPricer = FiniteDifference with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.Heston] SpotPrice: 80 GridProperties: [1x1 struct] DividendType: "continuous" DividendValue: 0.0200
Price Vanilla
Instrument
Use the following sensitivities when pricing the Vanilla
instrument.
InpSensitivity = ["delta", "gamma", "theta", "rho", "vega", "vegalt"];
Use price
to compute the price and sensitivities for the Vanilla
instrument that uses the NumericalIntegration
pricer.
[PriceNI, outPR_NI] = price(NIPricer,VanillaOpt,InpSensitivity)
PriceNI = 4.7007
outPR_NI = priceresult with properties: Results: [1x7 table] PricerData: []
Use price
to compute the price and sensitivities for the Vanilla
instrument that uses the FFT
pricer.
[PriceFFT, outPR_FFT] = price(FFTPricer,VanillaOpt,InpSensitivity)
PriceFFT = 4.7007
outPR_FFT = priceresult with properties: Results: [1x7 table] PricerData: []
Use price
to compute the price and sensitivities for the Vanilla
instrument that uses the FiniteDifference
pricer.
[PriceFD, outPR_FD] = price(FDPricer,VanillaOpt,InpSensitivity)
PriceFD = 4.7003
outPR_FD = priceresult with properties: Results: [1x7 table] PricerData: [1x1 struct]
Aggregate the price results.
[outPR_NI.Results;outPR_FFT.Results;outPR_FD.Results]
ans=3×7 table
Price Delta Gamma Theta Rho Vega VegaLT
______ _______ ________ _______ ______ ______ ______
4.7007 0.57747 0.03392 -4.8474 20.805 17.028 5.2394
4.7007 0.57747 0.03392 -4.8474 20.805 17.028 5.2394
4.7003 0.57722 0.035254 -4.8483 20.801 17.046 5.2422
Compute Option Price Surfaces
Use the price
function for the NumericalIntegration
pricer and the price
function for the FFT
pricer to compute the prices for a range of Vanilla
instruments.
Maturities = datemnth(Settle,(3:3:24)'); NumMaturities = length(Maturities); Strikes = (20:10:160)'; NumStrikes = length(Strikes); [Maturities_Full,Strikes_Full] = meshgrid(Maturities,Strikes); NumInst = numel(Strikes_Full); VanillaOptions(NumInst, 1) = fininstrument("vanilla",... "ExerciseDate", Maturities_Full(1), "Strike", Strikes_Full(1)); for instidx=1:NumInst VanillaOptions(instidx) = fininstrument("vanilla",... "ExerciseDate", Maturities_Full(instidx), "Strike", Strikes_Full(instidx)); end Prices_NI = price(NIPricer, VanillaOptions); Prices_FFT = price(FFTPricer, VanillaOptions); figure; surf(Maturities_Full,Strikes_Full,reshape(Prices_NI,[NumStrikes,NumMaturities])); title('Price (Numerical Integration)'); view(-112,34); xlabel('Maturity') ylabel('Strike')
figure; surf(Maturities_Full,Strikes_Full,reshape(Prices_FFT,[NumStrikes,NumMaturities])); title('Price (FFT)'); view(-112,34); xlabel('Maturity') ylabel('Strike')
More About
Vanilla Option
A vanilla option is a category of options that includes only the most standard components.
A vanilla option has an expiration date and straightforward strike price. American-style options and European-style options are both categorized as vanilla options.
The payoff for a vanilla option is as follows:
For a call:
For a put:
where:
St is the price of the underlying asset at time t.
K is the strike price.
For more information, see Vanilla Option.
Tips
After creating a Vanilla
instrument object, you can use setExercisePolicy
to
change the size of the options. For example, if you have the following
instrument:
VanillaOpt = fininstrument("Vanilla",'ExerciseDate',datetime(2021,5,1),'Strike',29,'OptionType',"put",'ExerciseStyle',"European")
Vanilla
instrument's size by changing the
ExerciseStyle
from "European"
to
"American"
, use setExercisePolicy
:VanillaOpt = setExercisePolicy(VanillaOpt,[datetime(2021,1,1) datetime(2022,1,1)],100,'American')
Version History
Introduced in R2020aR2022b: Serial date numbers not recommended
Although Vanilla
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.
See Also
Functions
Topics
- Price European Vanilla Call Options Using Black-Scholes Model and Different Equity Pricers
- Use Black-Scholes Model to Price Asian Options with Several Equity Pricers
- Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments
- Choose Instruments, Models, and Pricers
- Supported Exercise Styles
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