price
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
.
[
adds an optional argument to specify sensitivities.Price
,PriceResult
] = price(___,inpSensitivity
)
Examples
Use IRTree
Pricer and HullWhite
Model to Price FixedBondOption
Instrument
This example shows the workflow to price a FixedBondOption
instrument when you use a HullWhite
model and an IRTree
pricing method.
Create FixedBond
Instrument Object
Use fininstrument
to create a FixedBond
instrument object as the underlying bond.
BondInst = fininstrument("FixedBond",'Maturity',datetime(2029,9,15),'CouponRate',0.025,'Period', 1,'Name',"fixed_bond_instrument")
BondInst = FixedBond with properties: CouponRate: 0.0250 Period: 1 Basis: 0 EndMonthRule: 1 Principal: 100 DaycountAdjustedCashFlow: 0 BusinessDayConvention: "actual" Holidays: NaT IssueDate: NaT FirstCouponDate: NaT LastCouponDate: NaT StartDate: NaT Maturity: 15-Sep-2029 Name: "fixed_bond_instrument"
Create FixedBondOption
Instrument Object
Use fininstrument
to create a FixedBondOption
instrument object.
FixedBOption = fininstrument("FixedBondOption",'ExerciseDate',datetime(2025,9,15),'Strike',98,'Bond',BondInst,'Name',"fixed_bond_option_instrument")
FixedBOption = FixedBondOption with properties: OptionType: "call" ExerciseStyle: "european" ExerciseDate: 15-Sep-2025 Strike: 98 Bond: [1x1 fininstrument.FixedBond] Name: "fixed_bond_option_instrument"
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2019,9,15); Type = 'zero'; ZeroTimes = [calyears([1:10])]'; ZeroRates = [0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307 0.0310]'; ZeroDates = Settle + ZeroTimes; myRC = ratecurve('zero',Settle,ZeroDates,ZeroRates)
myRC = ratecurve with properties: Type: "zero" Compounding: -1 Basis: 0 Dates: [10x1 datetime] Rates: [10x1 double] Settle: 15-Sep-2019 InterpMethod: "linear" ShortExtrapMethod: "next" LongExtrapMethod: "previous"
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
HullWhiteModel = finmodel("HullWhite",'Alpha',0.01,'Sigma',0.05)
HullWhiteModel = HullWhite with properties: Alpha: 0.0100 Sigma: 0.0500
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object and use the ratecurve
object with the 'DiscountCurve'
name-value pair argument.
HWTreePricer = finpricer("irtree",'Model',HullWhiteModel,'DiscountCurve',myRC,'TreeDates',ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1x1 struct] TreeDates: [10x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]
HWTreePricer.Tree
ans = struct with fields:
tObs: [0 1 1.9973 2.9945 3.9918 4.9918 5.9891 6.9863 7.9836 8.9836]
dObs: [15-Sep-2019 15-Sep-2020 15-Sep-2021 15-Sep-2022 15-Sep-2023 15-Sep-2024 15-Sep-2025 15-Sep-2026 15-Sep-2027 15-Sep-2028]
CFlowT: {[10x1 double] [9x1 double] [8x1 double] [7x1 double] [6x1 double] [5x1 double] [4x1 double] [3x1 double] [2x1 double] [9.9809]}
Probs: {[3x1 double] [3x3 double] [3x5 double] [3x7 double] [3x9 double] [3x11 double] [3x13 double] [3x15 double] [3x17 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6] [2 3 4 5 6 7 8] [2 3 4 5 6 7 8 9 10] [2 3 4 5 6 7 8 9 10 11 12] [2 3 4 5 6 7 8 9 10 11 12 13 14] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16] [2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18]}
FwdTree: {1x10 cell}
RateTree: {1x10 cell}
Price FixedBondOption
Instrument
Use price
to compute the price and sensitivities for the FixedBondOption
instrument.
[Price, outPR] = price(HWTreePricer,FixedBOption,["all"])
Price = 11.1739
outPR = priceresult with properties: Results: [1x4 table] PricerData: [1x1 struct]
outPR.Results
ans=1×4 table
Price Delta Gamma Vega
______ _______ ______ ______
11.174 -272.19 3667.6 243.09
Input Arguments
inpInstrument
— Instrument object
Cap
object | Floor
object | Swaption
object | FixedBond
object | OptionEmbeddedFixedBond
object | OptionEmbeddedFloatBond
object | FixedBondOption
object | FloatBond
object | FloatBondOption
object
Instrument object, specified as scalar or a vector of previously created instrument
objects. Create the instrument objects using fininstrument
. The following
instrument objects are supported:
Data Types: object
inpSensitivity
— List of sensitivities to compute
[ ]
(default) | string array with values "Price"
, "Delta"
,
"Gamma"
, "Vega"
, and
"All"
| cell array of character vectors with values 'Price'
,
'Delta'
, 'Gamma'
, 'Vega'
, and
'All'
(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 with possible values of 'Price'
,
'Delta'
, 'Gamma'
, 'Vega'
, and
'All'
.
inpSensitivity = {'All'}
or inpSensitivity =
["All"]
specifies that the output is 'Delta'
,
'Gamma'
, 'Vega'
, and 'Price'
.
This is the same as specifying inpSensitivity
to include each
sensitivity.
The sensitivities supported depend on the inpInstrument
.
inpInstrument | Supported Sensitivities |
---|---|
Cap | {'delta','gamma','vega','price'} |
Floor | {'delta','gamma','vega','price'} |
Swaption | {'delta','gamma','vega','price'} |
FixedBond | {'delta','gamma','vega','price'} |
OptionEmbeddedFixedBond | {'delta','gamma','vega','price'} |
FixedBondOption | {'delta','gamma','vega','price'} |
FloatBond | {'delta','gamma','vega','price'} |
FloatBondOption | {'delta','gamma','vega','price'} |
OptionEmbeddedFloatBond | {'delta','gamma','vega','price'} |
Note
Sensitivities are calculated based on yield shifts of 1 basis point, where the ShiftValue = 1/10000. All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide the sensitivities by their respective instrument price.
Example: inpSensitivity =
{'delta','gamma','vega','price'}
Data Types: string
| cell
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 data that depends on the instrument that is being pricedFixedBond
,FloatBond
,FixedBondOption
, andOptionEmbeddedFixedBond
have the following shared fields forPriceResult.PricerData.PriceTree
:tObs
contains the observation times.Connect
contains the connectivity vectors. Each element in the cell array describes how nodes in that level connect to the next. For a given tree level, there areNumNodes
elements in the vector, and they contain the index of the node at the next level that the middle branch connects to. Subtracting 1 from that value indicates where the up-branch connects to, and adding 1 indicates where the down branch connects to.
The following additional fields for
PriceResult.PricerData.PriceTree
depend on the instrument
type:
PTree
contains the clean prices.AITree
contains the accrued interest.Probs
contains the probability arrays. Each element of the cell array contains the up, middle, and down transition probabilities for each node of the level.dObs
contains the date of each level of the tree.CFlowT
is a cell array with as many elements as levels of the tree. Each cell array element contains the time factors (tObs
) corresponding to its level of the tree and those levels ahead of it.FwdTree
contains the forward spot rate from one node to the next. The forward spot rate is defined as the inverse of the discount factor.ExTree
contains the exercise indicator arrays. Each element of the cell array is an array containing1
's where an option is exercised and0
's where it isn't.ProbTree
contains the probability of reaching each node from root node.ExProbTree
contains the exercise probabilities. Each element in the cell array is an array containing0
's where there is no exercise, or the probability of reaching that node where exercise happens.ExProbsByTreeLevel
is an array with each row holding the exercise probability for a given option at each tree observation time.
A FixedBond
instrument has
these additional fields within PriceResult.PricerData.PriceTree
:
PTree
AITree
Probs
.
A FloatBond
instrument has
these additional fields within PriceResult.PricerData.PriceTree
:
dObs
CFlowT
Probs
FwdTree
A FixedBondOption
instrument has these additional fields within
PriceResult.PricerData.PriceTree
:
PTree
Probs
ExTree
A OptionEmbeddedFixedBond
instrument has these additional fields within
PriceResult.PricerData.PriceTree
:
PTree
ExTree
ProbTree
ExProbTree
ExProbsByTreeLevel
The following table displays the PriceResult.PricerData.PriceTree
fields related to each instrument.
PriceResult.PricerData.PriceTree Fields | FixedBond | FloatBond | FixedBondOption | OptionEmbeddedFixedBond |
---|---|---|---|---|
tObs | ✓ | ✓ | ✓ | ✓ |
Connect | ✓ | ✓ | ✓ | ✓ |
PTree | ✓ | No | ✓ | ✓ |
AITree | ✓ | No | No | No |
Probs | ✓ | ✓ | ✓ | No |
dObs | No | ✓ | No | No |
CFlowT | No | ✓ | No | No |
FwdTree | No | ✓ | ✓ | ✓ |
ExTree | No | No | ✓ | ✓ |
ProbTree | No | No | No | ✓ |
ExProbTree | No | No | No | ✓ |
ExProbsByTreeLevel | No | No | No | ✓ |
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.
Version History
Introduced in R2020a
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