price
Compute price for interest-rate, equity, or credit derivative instrument with
Analytic
pricer
Since R2020a
Syntax
Description
[
computes the instrument price and related pricing information based on the pricing object
Price
,PriceResult
] = price(inpPricer
,inpInstrument
)inpPricer
and the instrument object
inpInstrument
.
The Analytic
pricer supports the following pricer objects:
[
adds an optional argument to specify sensitivities.Price
,PriceResult
] = price(___,inpSensitivity
)
Examples
Use BjerksundStensland
Pricer and BlackScholes
Model to Price Spread
Instrument
This example shows the workflow to price a European exercise Spread
instrument when you use a BlackScholes
model and a BjerksundStensland
pricing method.
Create Spread
Instrument Object
Use fininstrument
to create a Spread
instrument object.
SpreadOpt = fininstrument("Spread",'Strike',5,'ExerciseDate',datetime(2021,9,15),'OptionType',"put",'ExerciseStyle',"european",'Name',"spread_option")
SpreadOpt = Spread with properties: OptionType: "put" Strike: 5 ExerciseStyle: "european" ExerciseDate: 15-Sep-2021 Name: "spread_option"
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",'Volatility',[0.2,0.1])
BlackScholesModel = BlackScholes with properties: Volatility: [0.2000 0.1000] Correlation: [2x2 double]
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 BjerksundStensland
Pricer Object
Use finpricer
to create a BjerksundStensland
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",'Model',BlackScholesModel,'DiscountCurve',myRC,'SpotPrice',[100,105],'DividendValue',[0.09,0.17],'PricingMethod',"BjerksundStensland")
outPricer = BjerksundStensland with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: [100 105] DividendValue: [0.0900 0.1700] DividendType: "continuous"
Price Spread
Instrument
Use price
to compute the price and sensitivities for the Spread
instrument.
[Price, outPR] = price(outPricer,SpreadOpt,["all"])
Price = 7.0596
outPR = priceresult with properties: Results: [1x7 table] PricerData: []
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Theta Rho
______ ____________________ ______________________ __________________ ________________ ______ _______
7.0596 -0.23249 0.27057 0.0069887 0.0055319 -3.2932 3.8327 41.938 18.303 1.1011 -5.6943
Use Rubinstein
Pricer and BlackScholes
Model to Price the Absolute Return for Cliquet
Instruments
This example shows the workflow to price the absolute return for three Cliquet
instruments when you use a BlackScholes
model and a Rubinstein
pricing method.
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 Cliquet
Instrument Object
Use fininstrument
to create a Cliquet
instrument object for three Cliquet instruments.
ResetDates = Settle + years(0:0.25:1); CliquetOpt = fininstrument("Cliquet",ResetDates=ResetDates,InitialStrike=[140;150;160],ExerciseStyle="european",Name="cliquet_option")
CliquetOpt=3×1 Cliquet array with properties:
OptionType
ExerciseStyle
ResetDates
LocalCap
LocalFloor
GlobalCap
GlobalFloor
ReturnType
InitialStrike
Name
Create BlackScholes
Model Object
Use finmodel
to create a BlackScholes
model object.
BlackScholesModel = finmodel("BlackScholes",Volatility=0.28)
BlackScholesModel = BlackScholes with properties: Volatility: 0.2800 Correlation: 1
Create Rubinstein
Pricer Object
Use finpricer
to create a Rubinstein
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
outPricer = finpricer("analytic",DiscountCurve=myRC,Model=BlackScholesModel,SpotPrice=135,DividendValue=0.025,PricingMethod="Rubinstein")
outPricer = Rubinstein with properties: DiscountCurve: [1x1 ratecurve] Model: [1x1 finmodel.BlackScholes] SpotPrice: 135 DividendValue: 0.0250 DividendType: "continuous"
Price Cliquet
Instruments
Use price
to compute the price and sensitivities for the three Cliquet
instruments.
[Price, outPR] = price(outPricer,CliquetOpt,"all")
Price = 3×1
28.1905
25.3226
23.8168
outPR=3×1 priceresult array with properties:
Results
PricerData
outPR.Results
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
______ _______ ________ ______ ______ ______ ______
28.191 0.59697 0.020662 2.8588 105.38 60.643 -14.62
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
______ _______ ________ ______ ______ ______ _______
25.323 0.41949 0.016816 2.2364 100.47 55.367 -11.708
ans=1×7 table
Price Delta Gamma Lambda Vega Rho Theta
______ _______ ________ ______ ______ ______ ______
23.817 0.29729 0.011133 1.6851 93.219 51.616 -7.511
Use CMSConvexityHull
Pricer and CMSConvexityHull
Model to Price CMS
and CMSNote
Instruments
This example shows the workflow to price a CMS
and CMSNote
instrument when you use a CMSConvexityHull
model and a CMSConvexityHull
pricing method.
Create ratecurve
Object
Create a ratecurve
object using ratecurve
for the underlying interest-rate curve for the CMS
instrument.
Settle = datetime(2022,9,15); Type = 'zero'; ZeroTimes = [calmonths(6) calyears([1 2 3 4 5 7 10 20 30])]'; ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]'; ZeroDates = Settle + ZeroTimes; ZeroCurve = ratecurve('zero',Settle,ZeroDates,ZeroRates)
ZeroCurve = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10x1 datetime] Rates: [10x1 double] Settle: 15-Sep-2022 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create CMS
Instrument Object
Use fininstrument
to create a CMS
instrument object.
CMSInstrument = fininstrument("CMS",Maturity=datetime(2028,9,15),CMSReferenceTenor=10,LegRate=[0 0.01],LegType=["cms" "fixed"],Name="CMS instrument")
CMSInstrument = CMS with properties: CMSReferenceReset: 2 CMSReferenceTenor: 10 LegRate: [0 0.0100] LegType: ["cms" "fixed"] Reset: [2 2] Basis: [0 0] Notional: 100 LatestFloatingRate: [NaN NaN] LatestCMSRate: NaN ResetOffset: [0 0] DaycountAdjustedCashFlow: [0 0] ProjectionCurve: [0x0 ratecurve] BusinessDayConvention: ["actual" "actual"] Holidays: NaT EndMonthRule: [1 1] StartDate: NaT Maturity: 15-Sep-2028 Name: "CMS instrument"
Create CMSNote
Instrument Object
Use fininstrument
to create a CMSNote
instrument object.
CMSNoteInstrument = fininstrument("CMSNote",Maturity=datetime(2028,9,15),CMSReferenceTenor=10,Name="CMSNote instrument")
CMSNoteInstrument = CMSNote with properties: CMSReferenceReset: 2 CMSReferenceTenor: 10 Spread: 0 InitialCouponPeriod: 0 InitialCouponRate: 0 Period: 2 Basis: 0 Principal: 100 LatestFloatingRate: NaN LatestCMSRate: NaN ResetOffset: 0 DaycountAdjustedCashFlow: 0 ProjectionCurve: [0x0 ratecurve] BusinessDayConvention: "actual" Holidays: NaT EndMonthRule: 1 StartDate: NaT Maturity: 15-Sep-2028 Name: "CMSNote instrument"
Create CMSConvexityHull
Model Object
Use finmodel
to create a CMSConvexityHull
model object.
SwapStartDates = datetime(2022,3,15) + calmonths(0:6:13*6)'; FwdSwapVolatility = [37.5;38.7;39.3;39.5;39.4;39.3;39.2;... 39;38.8;38.5;38.3;38;37.8;37.7]./100; CMSConvexityHullModel = finmodel("CMSConvexityHull",CMSConvexityData=timetable(SwapStartDates,FwdSwapVolatility))
CMSConvexityHullModel = CMSConvexityHull with properties: CMSConvexityData: [14x3 timetable]
CMSConvexityHullModel.CMSConvexityData
ans=14×3 timetable
SwapStartDates FwdSwapVolatility FwdVolatility FwdSwapFwdCorrelation
______________ _________________ _____________ _____________________
15-Mar-2022 0.375 0 0
15-Sep-2022 0.387 0 0
15-Mar-2023 0.393 0 0
15-Sep-2023 0.395 0 0
15-Mar-2024 0.394 0 0
15-Sep-2024 0.393 0 0
15-Mar-2025 0.392 0 0
15-Sep-2025 0.39 0 0
15-Mar-2026 0.388 0 0
15-Sep-2026 0.385 0 0
15-Mar-2027 0.383 0 0
15-Sep-2027 0.38 0 0
15-Mar-2028 0.378 0 0
15-Sep-2028 0.377 0 0
Create CMSConvexityHull
Pricer Object
Use finpricer
to create a CMSConvexityHull
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value pair argument.
CMSConvexityHullPricer = finpricer("analytic",Model=CMSConvexityHullModel,DiscountCurve=ZeroCurve)
CMSConvexityHullPricer = CMSConvexityHull with properties: Model: [1x1 finmodel.CMSConvexityHull] DiscountCurve: [1x1 ratecurve]
Price CMS
and CMSNote
Instruments
Use price
to compute the price for the CMS
and CMSNote
instruments.
[CMSPrice, outPR] = price(CMSConvexityHullPricer,CMSInstrument)
CMSPrice = 11.5623
outPR = priceresult with properties: Results: [1x1 table] PricerData: [13x7 timetable]
outPR.PricerData % For the CMS instrument
ans=13×7 timetable
Time SwapStartDates ForwardSwapRates ConvexityAdjustments TimingAdjustments CMSRates Accruals SwapEndDates
___________ ______________ ________________ ____________________ _________________ ________ ________ ____________
15-Sep-2022 15-Sep-2022 0.021605 0 0 0.021605 0 15-Sep-2032
15-Mar-2023 15-Sep-2022 0.021605 0 0 0.021605 0.5 15-Sep-2032
15-Sep-2023 15-Mar-2023 0.02286 0.00019992 0 0.02306 0.5 15-Mar-2033
15-Mar-2024 15-Sep-2023 0.024135 0.00045273 0 0.024588 0.5 15-Sep-2033
15-Sep-2024 15-Mar-2024 0.025431 0.00074919 0 0.02618 0.5 15-Mar-2034
15-Mar-2025 15-Sep-2024 0.026751 0.0010992 0 0.02785 0.5 15-Sep-2034
15-Sep-2025 15-Mar-2025 0.02801 0.0014918 0 0.029502 0.5 15-Mar-2035
15-Mar-2026 15-Sep-2025 0.029262 0.0019316 0 0.031194 0.5 15-Sep-2035
15-Sep-2026 15-Mar-2026 0.030318 0.0023865 0 0.032705 0.5 15-Mar-2036
15-Mar-2027 15-Sep-2026 0.0313 0.0028593 0 0.03416 0.5 15-Sep-2036
15-Sep-2027 15-Mar-2027 0.032102 0.003331 0 0.035433 0.5 15-Mar-2037
15-Mar-2028 15-Sep-2027 0.032798 0.0038007 0 0.036599 0.5 15-Sep-2037
15-Sep-2028 15-Mar-2028 0.033406 0.0042947 0 0.0377 0.5 15-Mar-2038
[CMSNotePrice, outPR] = price(CMSConvexityHullPricer,CMSNoteInstrument)
CMSNotePrice = 109.1087
outPR = priceresult with properties: Results: [1x1 table] PricerData: [13x7 timetable]
outPR.PricerData % For the CMS Note instrument
ans=13×7 timetable
Time SwapStartDates ForwardSwapRates ConvexityAdjustments TimingAdjustments CMSRates Accruals SwapEndDates
___________ ______________ ________________ ____________________ _________________ ________ ________ ____________
15-Sep-2022 15-Sep-2022 0.021605 0 0 0.021605 0 15-Sep-2032
15-Mar-2023 15-Sep-2022 0.021605 0 0 0.021605 0.5 15-Sep-2032
15-Sep-2023 15-Mar-2023 0.02286 0.00019992 0 0.02306 0.5 15-Mar-2033
15-Mar-2024 15-Sep-2023 0.024135 0.00045273 0 0.024588 0.5 15-Sep-2033
15-Sep-2024 15-Mar-2024 0.025431 0.00074919 0 0.02618 0.5 15-Mar-2034
15-Mar-2025 15-Sep-2024 0.026751 0.0010992 0 0.02785 0.5 15-Sep-2034
15-Sep-2025 15-Mar-2025 0.02801 0.0014918 0 0.029502 0.5 15-Mar-2035
15-Mar-2026 15-Sep-2025 0.029262 0.0019316 0 0.031194 0.5 15-Sep-2035
15-Sep-2026 15-Mar-2026 0.030318 0.0023865 0 0.032705 0.5 15-Mar-2036
15-Mar-2027 15-Sep-2026 0.0313 0.0028593 0 0.03416 0.5 15-Sep-2036
15-Sep-2027 15-Mar-2027 0.032102 0.003331 0 0.035433 0.5 15-Mar-2037
15-Mar-2028 15-Sep-2027 0.032798 0.0038007 0 0.036599 0.5 15-Sep-2037
15-Sep-2028 15-Mar-2028 0.033406 0.0042947 0 0.0377 0.5 15-Mar-2038
Input Arguments
inpPricer
— Pricer object
BjerksundStensland
object | IkedaKunitomo
object | Black
object | BlackScholes
object | CDSBlack
object | CMSConvexityHull
object | ConzeViswanathan
object | GoldmanSosinGatto
object | HeynenKat
object | HullWhite
object | Heston
object | KemnaVorst
object | Kirk
object | Levy
object | Normal
object | Rubinstein
object | RollGeskeWhaley
object | SABR
object | TurnbullWakeman
object | JarrowYildirim
object
Pricer object (previously created using finpricer
), specified as a
scalar. The supported pricer objects are:
Data Types: object
inpInstrument
— Instrument object
Cap
object | CMS
object | CMSNote
object | Floor
object | Swaption
object | Vanilla
object | Lookback
object | PartialLookback
object | Barrier
object | DoubleBarrier
object | Asian
object | Spread
object | Cliquet
object | VarianceSwap
object | CDSOption
object | YearYearInflationCap
object | YearYearInflationFloor
object | YearYearInflationSwap
object | ZeroCouponInflationCap
object | ZeroCouponInflationFloor
object | ZeroCouponInflationSwap
object
Instrument object (previously created using fininstrument
), specified as
a scalar or a vector.
The supported instrument objects using a scalar or vector are:
The supported instrument object using a scalar is:
Data Types: object
inpSensitivity
— List of sensitivities to compute
[ ]
(default) | string array with values dependent on pricer object | cell array of character vectors with values dependent on pricer object
(Optional) List of sensitivities to compute, specified as a
NOUT
-by-1
or a
1
-by-NOUT
cell array of character vectors or
string array.
The supported sensitivities depend on the pricing method.
inpPricer Object | Supported Sensitivities |
---|---|
BjerksundStensland | {'delta','gamma','vega',
'theta','rho','price','lambda'} |
IkedaKunitomo | {'delta','gamma','vega','theta','rho','price','lambda'} |
Black | 'price' |
CMSConvexityHull | 'price' |
BlackScholes | {'delta','gamma','vega','theta','rho','price','lambda'} |
CDSBlack | 'price' |
ConzeViswanathan | {'delta','gamma','vega','theta','rho','price','lambda}' |
GoldmanSosinGatto | {'delta','gamma','vega','theta','rho','price','lambda}' |
HeynenKat | {'delta','gamma','vega','theta','rho','price','lambda}' |
HullWhite | 'price' |
Heston | 'price' |
KemnaVorst | {'delta','gamma','vega','theta','rho','price','lambda'} |
Kirk | {'delta','gamma','vega','theta','rho','price','lambda'} |
Levy | {'delta','gamma','vega','theta','rho','price','lambda'} |
Normal | 'price' |
RollGeskeWhaley | {'delta','gamma','vega','theta','rho','price','lambda'} |
Rubinstein | {'delta','gamma','vega','theta','rho','price','lambda'} |
SABR | 'price' |
TurnbullWakeman | {'delta','gamma','vega','theta','rho','price',} |
JarrowYildirim | 'price' |
inpSensitivity = {'All'}
or inpSensitivity =
["All"]
specifies that all sensitivities for the pricing method are
returned. This is the same as specifying inpSensitivity
to include
each sensitivity.
Example: inpSensitivity =
["delta","gamma","vega","lambda","rho","theta","price"]
Data Types: cell
| string
Output Arguments
Price
— Instrument price
numeric
Instrument price, returned as a numeric.
PriceResult
— Price result
PriceResult
object
Price result, returned as a PriceResult
object. The object has
the following fields:
PriceResult.Results
— Table of results that includes sensitivities (if you specifyinpSensitivity
)PriceResult.PricerData
— Structure for pricer dataNote
When pricing a
VarianceSwap
,PriceResult.FairVariance
is returned.
Note
The inpPricer
options that do not support sensitivities do
not return a PriceResult
. For example, there is no
PriceResult
returned for when using a Black
,
CDSBlack
, HullWhite
,
Normal
, Heston
, SABR
, or
JarrowYildirim
pricing method.
More About
Delta
A delta sensitivity measures the rate at which the price of an option is expected to change relative to a $1 change in the price of the underlying asset.
Delta is not a static measure; it changes as the price of the underlying asset changes (a concept known as gamma sensitivity), and as time passes. Options that are near the money or have longer until expiration are more sensitive to changes in delta.
Gamma
A gamma sensitivity measures the rate of change of an option's delta in response to a change in the price of the underlying asset.
In other words, while delta tells you how much the price of an option might move, gamma tells you how fast the option's delta itself will change as the price of the underlying asset moves. This is important because this helps you understand the convexity of an option's value in relation to the underlying asset's price.
Vega
A vega sensitivity measures the sensitivity of an option's price to changes in the volatility of the underlying asset.
Vega represents the amount by which the price of an option would be expected to change for a 1% change in the implied volatility of the underlying asset. Vega is expressed as the amount of money per underlying share that the option's value will gain or lose as volatility rises or falls.
Theta
A theta sensitivity measures the rate at which the price of an option decreases as time passes, all else being equal.
Theta is essentially a quantification of time decay, which is a key concept in options pricing. Theta provides an estimate of the dollar amount that an option's price would decrease each day, assuming no movement in the price of the underlying asset and no change in volatility.
Rho
A rho sensitivity measures the rate at which the price of an option is expected to change in response to a change in the risk-free interest rate.
Rho is expressed as the amount of money an option's price would gain or lose for a one percentage point (1%) change in the risk-free interest rate.
Lambda
A lambda sensitivity measures the percentage change in an option's price for a 1% change in the price of the underlying asset.
Lambda is a measure of leverage, indicating how much more sensitive an option is to price movements in the underlying asset compared to owning the asset outright.
Version History
Introduced in R2020aR2023b: Support for Pricing Inflation Instruments Using JarrowYildirim
Pricer
You can use the price function to calculate the price of a YearYearInflationCap
, YearYearInflationFloor
, ZeroCouponInflationCap
, or ZeroCouponInflationFloor
using a JarrowYildirim
model object
and a JarrowYildirim
pricing method.
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