oas
Compute option adjusted spread for OptionEmbeddedFixedBond
instrument using interest-rate tree
Since R2023a
Description
[
computes the option adjusted spread (OAS), option adjusted duration (OAD), and option
adjusted convexity (OAC) of an OAS
,OAD
,OAC
] = oas(IRTreePricer
,OptionEmbeddedFixedBondInstrument
,MarketPrice
)OptionEmbeddedFixedBond
instrument using a HullWhite
, BlackKarasinski
, or
BlackDermanToy
model with
an IRTree
pricer.
Examples
Compute OAS for OptionEmbeddedFixedBond
Instruments Using HullWhite
Model and IRTree
Pricer
This example shows how to compute the option adjusted spread (OAS) with American, European, and Bermudan exercise styles for three callable OptionEmbeddedFixedBond
instruments. For this example, you use a HullWhite
model and an IRTree
pricing method.
Create ratecurve
Object
Create a ratecurve
object using ratecurve
.
Settle = datetime(2018,1,1);
ZeroTimes = calyears(1:10)';
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = Settle + ZeroTimes;
Compounding = 1;
ZeroCurve = ratecurve("zero",Settle,ZeroDates,ZeroRates,Compounding=Compounding);
Create OptionEmbeddedFixedBond
Instrument Objects
Use fininstrument
to create two OptionEmbeddedFixedBond
instrument objects with the three different exercise styles.
Maturity = datetime(2024,1,1); % Option embedded bond (American callable bond) Strike = 100; ExerciseDates = datetime(2024,1,1); CallSchedule = timetable(ExerciseDates,Strike,VariableNames={'Strike Schedule'}); Period = 1; CallableBondAmerican = fininstrument("OptionEmbeddedFixedBond",Maturity=Maturity, ... CouponRate=0.025,Period=Period, ... CallSchedule=CallSchedule,CallExerciseStyle="american")
CallableBondAmerican = OptionEmbeddedFixedBond 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: 01-Jan-2024 CallDates: 01-Jan-2024 PutDates: [0x1 datetime] CallSchedule: [1x1 timetable] PutSchedule: [0x0 timetable] CallExerciseStyle: "american" PutExerciseStyle: [0x0 string] Name: ""
% Option embedded bond (European callable bond) Strike = 100; ExerciseDates = datetime(2024,1,1); CallSchedule = timetable(ExerciseDates,Strike,VariableNames={'Strike Schedule'}); Period = 1; CallableBondEuropean = fininstrument("OptionEmbeddedFixedBond",Maturity=Maturity,... CouponRate=0.025,Period=Period, ... CallSchedule=CallSchedule)
CallableBondEuropean = OptionEmbeddedFixedBond 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: 01-Jan-2024 CallDates: 01-Jan-2024 PutDates: [0x1 datetime] CallSchedule: [1x1 timetable] PutSchedule: [0x0 timetable] CallExerciseStyle: "european" PutExerciseStyle: [0x0 string] Name: ""
% Option embedded bond (Bermudan callable bond) Strike = [100; 100]; ExerciseDates = [datetime(2020,1,1); datetime(2024,1,1)]; Period = 1; CallSchedule = timetable(ExerciseDates,Strike,VariableNames={'Strike Schedule'}); CallableBondBermudan = fininstrument("OptionEmbeddedFixedBond",Maturity=Maturity, ... CouponRate=0.025,Period=Period, ... CallSchedule=CallSchedule,CallExerciseStyle="bermudan")
CallableBondBermudan = OptionEmbeddedFixedBond 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: 01-Jan-2024 CallDates: [2x1 datetime] PutDates: [0x1 datetime] CallSchedule: [2x1 timetable] PutSchedule: [0x0 timetable] CallExerciseStyle: "bermudan" PutExerciseStyle: [0x0 string] Name: ""
Create HullWhite
Model Object
Use finmodel
to create a HullWhite
model object.
VolCurve = 0.01;
AlphaCurve = 0.1;
HWModel = finmodel("HullWhite",alpha=AlphaCurve,sigma=VolCurve);
Create IRTree
Pricer Object
Use finpricer
to create an IRTree
pricer object and use the ratecurve
object for the 'DiscountCurve'
name-value argument.
HWTreePricer = finpricer("IRTree",Model=HWModel,DiscountCurve=ZeroCurve,TreeDates=ZeroDates)
HWTreePricer = HWBKTree with properties: Tree: [1x1 struct] TreeDates: [10x1 datetime] Model: [1x1 finmodel.HullWhite] DiscountCurve: [1x1 ratecurve]
Compute OAS for OptionEmbeddedFixedBond
Instruments
Use oas
to compute the OAS
, OAD
, and OAC
for the three OptionEmbeddedFixedBond
instruments.
MarketPriceAmerican = 98; MarketPrice = 105.25; [OAS,OAD,OAC] = oas(HWTreePricer,CallableBondAmerican,MarketPriceAmerican)
OAS = 0.0139
OAD = 3.9445
OAC = 11.7023
[OAS,OAD,OAC] = oas(HWTreePricer,CallableBondEuropean,MarketPrice)
OAS = 0.0041
OAD = 5.5673
OAC = 18.7972
[OAS,OAD,OAC] = oas(HWTreePricer,CallableBondBermudan,MarketPrice)
OAS = -0.0072
OAD = 2.0486
OAC = 3.2698
Input Arguments
IRTreePricer
— Pricer object
IRTree
object
Pricer object, specified as a scalar IRTree
pricer object. Use
finpricer
to create the IRTree
pricer object.
Note
The IRTree
pricer must use a HullWhite
, BlackKarasinski
, or
BlackDermanToy
model.
Data Types: object
OptionEmbeddedFixedBondInstrument
— Instrument object
OptionEmbeddedFixedBond
object
OptionEmbeddedFixedBond
instrument object, specified as scalar or
a vector of previously created instrument objects. Create the instrument objects using
fininstrument
and OptionEmbeddedFixedBond
.
Data Types: object
MarketPrice
— Market price of OptionEmbeddedFixedBond
instrument
scalar numeric | vector of numeric values
Market price of OptionEmbeddedFixedBond
instrument, specified as
a scalar numeric or N
-by-1
vector of numeric
values.
Data Types: double
Output Arguments
OAS
— Option adjusted spread
numeric decimal
Option adjusted spread (OAS), returned as a numeric decimal value.
OAD
— Option adjusted duration
numeric decimal
Option adjusted duration (OAD), returned as a numeric decimal value.
OAC
— Option adjusted convexity
numeric decimal
Option adjusted convexity (OAC), returned as a numeric decimal value.
More About
Option Adjusted Spread
Option adjusted spread (OAS) adjusts a bond spread for the option's value and is the standard measure for valuing and comparing bonds with different redemption structures.
OAS is a measure of yield spread that accounts for embedded call or put options in the valuation of bonds. The computation of OAS is similar to computing the bond spread, with the difference being that the cash flows are nondeterministic. In other words, the OAS computation considers the possibility of a change in the bond’s cash flows due to early redemptions. To compute an OAS, you must model the future behavior of interest rates.
In general, bonds with similar characteristics and credit risks should have the same OAS. If a bond has an OAS higher than the OAS of its peers (bond with similar characteristics and credit quality), it is considered undervalued. Conversely, a bond with a low OAS relative to its peers is considered overvalued.
Option Adjusted Duration
Option adjusted duration (OAD) accounts for the effect of the call option on the expected life of a bond.
OAD weighs the probability that the bond will be called based on the spread between its coupon rate and its yield, as well as the volatility of interest rates. Generally speaking, option adjusted duration (OAD) is longer than modified duration when a bond is priced to a call date, and shorter than modified duration when a bond is priced to maturity.
Option Adjusted Convexity
Option adjusted convexity (OAC) is a measure of a bond's convexity, which account for the convexity of options embedded within the bond.
OAC captures the curvature of the price and yield relationship observed in bonds. Low values mean the relationship is near to linearity (a change in the price leads to a proportional change in the yield). The OAC can vary from the negative to the positive, depending on the yield’s amount and the time to call or time to put. In contrast with modified convexity, OAC assumes that the cash flows of a bond change when yields change.
Version History
Introduced in R2023a
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