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oasbybk

Determine option adjusted spread using Black-Karasinski model

Syntax

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

Description

example

[OAS,OAD,OAC] = oasbybk(BKTree,Price,CouponRate,Settle,Maturity,OptSpec,Strike,ExerciseDates) calculates option adjusted spread using a Black-Karasinski model.

example

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

Examples

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This example shows how to compute OAS and OAD using the Black-Karasinski (BK) model using the following data.

ValuationDate = 'Aug-2-2010';
Rates = [0.0355; 0.0382; 0.0427; 0.0489];
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 = 0.10;
Alpha = 0.01;
VS = bkvolspec(ValuationDate, EndDates, Sigma*ones(size(EndDates)),...
EndDates, Alpha*ones(size(EndDates)));
TS = bktimespec(ValuationDate, EndDates, Compounding);

% build the BK tree
BKTree = bktree(VS, RateSpec, TS);

% instrument information
CouponRate = 0.045;
Settle = ValuationDate;
Maturity = '02-Aug-2014';
OptSpec = 'put';
Strike = 100;
ExerciseDates ='02-Aug-2013';
Period = 1;
AmericanOpt = 1;
Price = 101;

% compute OAS and OAD
[OAS, OAD] = oasbybk(BKTree, Price, CouponRate, Settle, Maturity,...
OptSpec, Strike, ExerciseDates, 'Period', Period, 'AmericanOpt', AmericanOpt)
OAS = 21.8655
OAD = 1.8654

Input Arguments

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Interest-rate tree structure, specified by using bktree.

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 of serial date numbers or date character vectors.

Note

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

Data Types: double | char

Maturity date, specified as an NINST-by-1 vector of serial date numbers or date character vectors.

Data Types: double | char

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 using serial date numbers 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.

Data Types: double | char

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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

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Option type, specified as NINST-by-1 positive integer flags with values:

  • 0 — European/Bermuda

  • 1 — American

Data Types: double

Coupons per year, specified as an NINST-by-1 vector.

Data Types: double

Day-count basis, specified as 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 is specified as 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 an NINST-by-1 vector using serial date numbers or date character vectors.

Data Types: double | char

Irregular first coupon date, specified as an NINST-by-1 vector using serial date numbers date or date character vectors.

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.

Data Types: double | char

Irregular last coupon date, specified as a NINST-by-1 vector using serial date numbers or date character vectors.

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.

Data Types: char | double

Forward starting date of payments (the date from which a bond cash flow is considered), specified as a NINST-by-1 vector using serial date numbers or date character vectors.

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

Data Types: char | double

Face or par value, specified as anNINST-by-1 vector.

Data Types: double

Derivatives pricing options, specified as structure that is created with derivset.

Data Types: struct

Output Arguments

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Option adjusted spread, 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

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Bond with Embedded Options

A bond with embedded option allows the issuer to buy back (callable) or redeem (puttable) the bond at a predetermined price at specified future dates.

Financial Instruments Toolbox™ software supports American, European, and Bermuda callable and puttable bonds. The pricing for a bond with embedded options is as follows:

  • Callable bond — The holder bought a bond and sold a call option to the issuer. For example, if interest rates go down by the time of the call date, the issuer is able to refinance its debt at a cheaper level and can call the bond. The price of a callable bond is:

    Price callable bond = Price Option free bondPrice call option

  • Puttable bond — The holder bought a bond and a put option. For example, if interest rates rise, the future value of coupon payments becomes less valuable. Therefore, the investor can sell the bond back to the issuer and then lend proceeds elsewhere at a higher rate. The price of a puttable bond is:

    Price puttable bond = Price Option free bond + Price put option

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.

Introduced in R2011a

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