oasbybdt - Determine option adjusted spread using Black-Derman-Toy model

Syntax

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

Description

[OAS, OAD, OAC] = oasbybdt(BDTTree, Price, CouponRate, Settle, Maturity, OptSpec, Strike, ExerciseDates) calculates option adjusted spread (OAS), duration (OAD), and convexity (OAC) using a BDT model.

[OAS, OAD, OAC] = oasbybdt(BDTTree, Price, CouponRate, Settle, Maturity, OptSpec, Strike, ExerciseDates, Name,Value) calculates option adjusted spread (OAS), duration (OAD), and convexity (OAC) using a BDT model with additional options specified by one or more Name,Value pair arguments.

Input Arguments

`BDTTree`	Interest-rate tree structure created by `bdttree`.
`Price`	`NINST`-by-`1` vector of market prices of bonds with embedded options.
`CouponRate`	`NINST`-by-`1` vector for decimal annual rate.
`Settle`	`NINST`-by-`1` vector for settlement date.
`Maturity`	`NINST`-by-`1` vector for maturity date.
`OptSpec`	`NINST`-by-`1` cell array of strings for `'call'` or `'put'`.
`Strike`	Matrix of strike price values for supported option types: 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 `NaN`s. American option: `NINST`-by-`1` vector of strike price values for each option.
`ExerciseDates`	Matrix of exercise callable or puttable dates for supported option types: `NINST`-by-`1` (European option) or `NINST`-by-`NSTRIKES` (Bermuda option) matrix of exercise dates. Each row is the schedule for one option. For a European option, there is only one exercise date, the option expiry date. American option: `NINST`-by-`2` vector of exercise date boundaries. For each instrument, the option is exercised on any coupon date between or including the pair of dates on that row. If only one non-`NaN` date is listed, or if `ExerciseDates` is `NINST`-by-`1`, the option is exercised between the underlying bond `Settle` and the single listed exercise date.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments, where 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.

`'AmericanOpt'`	`NINST`-by-`1` vector for option flags: `0` (European/Bermuda) or `1` (American). Default: `0` (European/Bermuda)
`'Basis'`	Day-count basis of the instrument. A vector of integers. 0 = actual/actual 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (BMA) 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/actual (ISDA) 13 = BUS/252 For more information, see basis. Default: `0` (actual/actual)
`'EndMonthRule'`	`NINST`-by-1 vector for end-of-month rule. Values are `1` (in effect) and `0` (not in effect). Default: `1` (in effect)
`'IssueDate'`	`NINST`-by-`1` vector of bond issue date. Default: If you do not specify an `IssueDate`, the cash flow payment dates are determined from other inputs.
`'Face'`	`NINST`-by-`1` vector for face value. Default: `100`
`'FirstCouponDate'`	`NINST`-by-`1` vector. Date when a bond makes its first coupon payment; used when bond has an irregular first coupon period. When `FirstCouponDate` and `LastCouponDate` are both specified, `FirstCouponDate` takes precedence in determining the coupon payment structure. Default: If you do not specify a `FirstCouponDate`, the cash flow payment dates are determined from other inputs.
`'LastCouponDate'`	`NINST`-by-`1` vector. Last coupon date of a bond before the maturity date; used when bond has an irregular last coupon period. 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. Default: If you do not specify a `LastCouponDate`, the cash flow payment dates are determined from other inputs.
`'Period'`	`NINST`-by-`1` vector for coupons per year. Default: `2` per year
`'Options'`	Structure created with `derivset` containing derivatives pricing options. Default: None

Output Arguments

`OAS`	`NINST`-by-`1` vector for option adjusted spread.
`OAD`	`NINST`-by-`1` vector for option adjusted duration.
`OAC`	`NINST`-by-`1` vector for option adjusted convexity.

Definitions

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 Derivatives 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 bond − Price 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

Examples

Compute OAS using the Black-Derman-Toy (BDT) model with:

ValuationDate = 'Oct-1-2010';
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 VolsSpec 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 = '01-Oct-2014';
OptSpec = 'call';
Strike = 100;
ExerciseDates ='01-Oct-2011';
Period = 1;
Price = 101.58;

% Compute the OAS
OAS = oasbybdt(BDTTree, Price, CouponRate, Settle, Maturity,...
OptSpec, Strike, ExerciseDates, 'Period', Period)

OAS =

   36.5591

Use treeviewer to observe the tree you created:

treeviewer(BDTTree)

References

Fabozzi, F., Handbook of Fixed Income Securities, McGraw-Hill, 7th edition, 2005.

Windas, T., Introduction to Option-Adjusted Spread Analysis, Bloomberg Press, 3rd edition, 2007.

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