oasbybdt

Determine option adjusted spread using Black-Derman-Toy model

collapse all in page

Syntax

[OAS,OAD,OAC] = oasbybdt(BDTTree,Price,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates)
[OAS,OAD,OAC] = oasbybdt(___,Name,Value)

Description

[OAS,OAD,OAC] = oasbybdt(BDTTree,Price,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates) calculates option adjusted spread using a Black-Derman-Toy model.

oasbybdt computes prices of vanilla bonds with embedded options, stepped coupon bonds with embedded options, amortizing bonds with embedded options, and sinking fund bonds with call embedded option. For more information, see More About.

Note

Alternatively, you can use oas with an OptionEmbeddedFixedBond instrument using an IRTree pricer and a BlackDermanToy model. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

example

[OAS,OAD,OAC] = oasbybdt(___,Name,Value) adds optional name-value pair arguments.

example

Examples

collapse all

Open Live Script

This example shows how to compute OAS using the Black-Derman-Toy (BDT) model with the following data.

ValuationDate = datetime(2010,10,1);
Rates = [0.035; 0.042; 0.047; 0.052];
StartDates = ValuationDate;
EndDates = datemnth(ValuationDate, 12:12:48)';
Compounding = 1;
% define RateSpec
RateSpec = intenvset('ValuationDate', ValuationDate,...
'StartDates', StartDates, 'EndDates', EndDates, ...
'Rates', Rates, 'Compounding', Compounding); 

% specify VolSpec and TimeSpec
Sigma = 0.20;
VS = bdtvolspec(ValuationDate, EndDates, Sigma*ones(size(EndDates)));
TS = bdttimespec(ValuationDate, EndDates, Compounding);

% build the BDT tree
BDTTree = bdttree(VS, RateSpec, TS);
BDTTreenew = cvtree(BDTTree);

% instrument information
CouponRate = 0.065;
Settle = ValuationDate;
Maturity = datetime(2014,10,1);
OptSpec = 'call';
Strike = 100;
ExerciseDates = datetime(2011,10,1);
Period = 1;
Price = 101.58;

% compute the OAS
OAS = oasbybdt(BDTTree, Price, CouponRate, Settle, Maturity,...
OptSpec, Strike, ExerciseDates, 'Period', Period)
OAS = 
32.7688
Open Live Script

This example shows how to compute the OAS for an amortizing callable bond using a BDT lattice model.

Create a RateSpec.

Rates = [0.025;0.028;0.030;0.031];
ValuationDate = 'Jan-1-2018';
StartDates = ValuationDate;
EndDates = {'Jan-1-2019'; 'Jan-1-2020'; 'Jan-1-2021'; 'Jan-1-2022'};
Compounding = 1;
RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates',...
StartDates, 'EndDates', EndDates, 'Rates', Rates, 'Compounding', Compounding);

Build a BDT tree and assume a volatility of 5%.

Sigma = 0.05;  
BDTTimeSpec = bdttimespec(ValuationDate, EndDates);
BDTVolSpec = bdtvolspec(ValuationDate, EndDates, Sigma*ones(1, length(EndDates))');
BDTT = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec);

Define the callable bond.

CouponRate = 0.05;
Settle = 'Jan-1-2018';
Maturity =  'Jan-1-2021';
Period = 1;
    
    Face = { 
                 {'Jan-1-2019'  100; 
                  'Jan-1-2020'   70; ...
                   'Jan-1-2021'   50};
                 };
 
OptSpec = 'call'; 
Strike = [97 95 93];
ExerciseDates ={'Jan-1-2019' 'Jan-1-2020' 'Jan-1-2021'};

Compute the OAS for a callable amortizing bond using the BDT tree.

Price = 99;
BondType = 'amortizing';
OAS = oasbybdt(BDTT, Price, CouponRate, Settle, Maturity,...
OptSpec, Strike, ExerciseDates, 'Period', Period, 'Face', Face,'BondType', BondType)
OAS = 
53.0303

Input Arguments

collapse all

Interest-rate tree structure, specified by using bdttree.

Data Types: struct

Market prices of bonds with embedded options, specified as an NINST-by-1 vector.

Data Types: double

Bond coupon rate, specified as an NINST-by-1 decimal annual rate.

Data Types: double

Settlement date for the bond option, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

Note

The Settle date for every bond with an embedded option is set to the ValuationDate of the BDT tree. The bond argument Settle is ignored.

To support existing code, oasbybdt also accepts serial date numbers as inputs, but they are not recommended.

Maturity date, specified as an NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, oasbybdt also accepts serial date numbers as inputs, but they are not recommended.

Definition of option, specified as a NINST-by-1 cell array of character vectors.

Data Types: char | cell

Option strike price value, specified as a NINST-by-1 or NINST-by-NSTRIKES depending on the type of option:

  • European option — NINST-by-1 vector of strike price values.

  • Bermuda option — NINST by number of strikes (NSTRIKES) matrix of strike price values. Each row is the schedule for one option. If an option has fewer than NSTRIKES exercise opportunities, the end of the row is padded with NaNs.

  • American option — NINST-by-1 vector of strike price values for each option.

Data Types: double

Option exercise dates, specified as a NINST-by-1, NINST-by-2, or NINST-by-NSTRIKES vector using a datetime array, string array, or date character vectors, depending on the type of option:

  • For a European option, use a NINST-by-1 vector of dates. For a European option, there is only one ExerciseDates on the option expiry date.

  • For a Bermuda option, use a NINST-by-NSTRIKES vector of dates. Each row is the schedule for one option.

  • For an American option, use a NINST-by-2 vector of exercise date boundaries. The option can be exercised on any date between or including the pair of dates on that row. If only one non-NaN date is listed, or if ExerciseDates is a NINST-by-1 vector, the option is exercised between the underlying bond Settle date and the single listed exercise date.

To support existing code, oasbybdt also accepts serial date numbers as inputs, but they are not recommended.

Name-Value Arguments

collapse all

Specify 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: OAS = oasbybdt(BDTTree,Price,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates,'Period',4)

Option type, specified as the comma-separated pair consisting of 'AmericanOpt' and NINST-by-1 positive integer flags with values:

  • 0 — European/Bermuda

  • 1 — American

Data Types: double

Coupons per year, specified as the comma-separated pair consisting of 'Period' and a NINST-by-1 vector.

Data Types: double

Day-count basis, specified as the comma-separated pair consisting of 'Basis' and a NINST-by-1 vector of integers.

  • 0 = actual/actual

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (PSA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see Basis.

Data Types: double

End-of-month rule flag, specified as the comma-separated pair consisting of 'EndMonthRule' and a nonnegative integer using a NINST-by-1 vector. This rule applies only when Maturity is an end-of-month date for a month having 30 or fewer days.

  • 0 = Ignore rule, meaning that a bond coupon payment date is always the same numerical day of the month.

  • 1 = Set rule on, meaning that a bond coupon payment date is always the last actual day of the month.

Data Types: double

Bond issue date, specified as the comma-separated pair consisting of 'IssueDate' and a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, oasbybdt also accepts serial date numbers as inputs, but they are not recommended.

Irregular first coupon date, specified as the comma-separated pair consisting of 'FirstCouponDate' and a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, oasbybdt also accepts serial date numbers as inputs, but they are not recommended.

When FirstCouponDate and LastCouponDate are both specified, FirstCouponDate takes precedence in determining the coupon payment structure. If you do not specify a FirstCouponDate, the cash flow payment dates are determined from other inputs.

Irregular last coupon date, specified as the comma-separated pair consisting of 'LastCouponDate' and a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, oasbybdt also accepts serial date numbers as inputs, but they are not recommended.

In the absence of a specified FirstCouponDate, a specified LastCouponDate determines the coupon structure of the bond. The coupon structure of a bond is truncated at the LastCouponDate, regardless of where it falls, and is followed only by the bond's maturity cash flow date. If you do not specify a LastCouponDate, the cash flow payment dates are determined from other inputs.

Forward starting date of payments (the date from which a bond cash flow is considered), specified as the comma-separated pair consisting of 'StartDate' and a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, oasbybdt also accepts serial date numbers as inputs, but they are not recommended.

If you do not specify StartDate, the effective start date is the Settle date.

Face or par value, specified as the comma-separated pair consisting of 'Face' and a NINST-by-1 vector or a NINST-by-1 cell array where each element is a NumDates-by-2 cell array where the first column is dates using a datetime, string, or date character vector, and the second column is associated face value. The date indicates the last day that the face value is valid.

Data Types: double | string | char | datetime

Type of underlying bond, specified as the comma-separated pair consisting of 'BondType' and a NINST-by-1 cell array of character vectors or string array specifying if the underlying is a vanilla bond, an amortizing bond, or a callable sinking fund bond. The supported types are:

  • 'vanilla' is a standard callable or puttable bond with a scalar Face value and a single coupon or stepped coupons.

  • 'callablesinking' is a bond with a schedule of Face values and a sinking fund call provision with a single or stepped coupons.

  • 'amortizing' is an amortizing callable or puttable bond with a schedule of Face values with single or stepped coupons.

Data Types: char | string

Derivatives pricing options, specified as the comma-separated pair consisting of 'Options' and a structure that is created with derivset.

Data Types: struct

Output Arguments

collapse all

Option adjusted spread in basis points, returned as a NINST-by-1 vector.

Option adjusted duration, returned as a NINST-by-1 vector.

Option adjusted convexity, returned as a NINST-by-1 vector.

More About

collapse all

References

[1] Fabozzi, F. Handbook of Fixed Income Securities. 7th Edition. McGraw-Hill, 2005.

[2] Windas, T. Introduction to Option-Adjusted Spread Analysis. 3rd Edition. Bloomberg Press, 2007.

Version History

Introduced in R2011a

expand all

See Also

| | | | | |

Topics