MATLAB: How to price an existing bond using the FLOATBYZERO function in the Financial Derivatives Toolbox

dateFinancial Derivatives Toolboxfloatfloatbyzerointenvsetpriceratespecsettlementvaluation

I would like to price the following bond using the FLOATBYZERO function:

The spread of the bond is 50bp. It is an existing floating bond which was issued two years ago. The last reset is 12/31/2004 and it will mature 12/31/2010. I would like to find the price of this bond on 4/5/2005.

Best Answer

The following code uses the FLOATBYZERO function to meet the bond specification:

Spread   = 50;
Maturity = '12-31-2010';
Settle   = '04-05-2005';
RateData = [datenum('12/31/2004')  datenum('6/30/2005')   2.78
              datenum(  '4/5/2005')  datenum('10/5/2005')   3.38
              datenum(  '4/5/2005')  datenum( '4/5/2006')   3.79
              datenum(  '4/5/2005')  datenum( '4/5/2007')   4.16
              datenum(  '4/5/2005')  datenum( '4/5/2008')   4.36
              datenum(  '4/5/2005')  datenum( '4/5/2010')   4.59
              datenum(  '4/5/2005')  datenum( '4/5/2012')   4.76
              datenum(  '4/5/2005')  datenum( '4/5/2015')   4.94];
StartDates = RateData(:,1);
EndDates   = RateData(:,2);
Rates      = RateData(:,3) / 100;
RateSpec = intenvset('ValuationDate', '12-31-2004', 'StartDates',StartDates, 'EndDates', EndDates, 'Rates', Rates)
Price = floatbyzero(RateSpec, Spread, Settle, Maturity, 2)

Related Solutions

MATLAB: What is the difference between IMPVBYBLS and BLSIMPV, and how to I determine the Black-Scholes implied volatility using these functions

Both IMPVBYBLS and BLSIMPV use the Black-Scholes model to compute the implied volatility for a given option price. However, one of the main differences between the two functions is that IMPVBYBLS allows specifying cash dividends as well as continuous dividend yields, while BLSIMPV only allows continuous dividend yields.

If you specify continuous dividend yields for both IMPVBYBLS and BLSIMPV, they produce the same results:

Strike = 29;
AssetPrice = 30;
Sigma = .25;
Rates = 0.05;
Settle = datenum('01-Jan-2008');
Maturity = datenum('01-May-2008');
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, ...
'EndDates',Maturity, 'Rates', Rates, 'Compounding', -1,'Basis',1);
DividendType = {'continuous';'continuous'};
DividendAmounts = [0.05; 0.045];
ExDividendDates = {NaN;NaN};
StockSpec = stockspec(Sigma, AssetPrice, DividendType, DividendAmounts);
OptSpec = {'call'; 'put'};
OptionPrice = optstockbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, Strike);
ImpvVol1 = impvbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec, ...
Strike, OptionPrice)
ImpvVol2 = blsimpv(AssetPrice, Strike, Rates, ...
yearfrac(Settle,Maturity,1), OptionPrice, 'Class', OptSpec,'Yield',DividendAmounts)
ImpvVol1 =
0.250000000000000
0.250000000000000
ImpvVol2 =
0.250000000000000
0.250000000000000

MATLAB: How the oasbyhw function supports for stepped coupon bonds

The help documentation for "oasbyhw" function doesn't provide an example of how to use stepped coupon bonds. Below is a simple demo that could help you understand the usage of this feature, the key part is providing the coupon schedule as part of the "CouponRate" input.

% Zero Curve
Settle = datenum('15-Jun-2020');
ZeroRates = [0.0052 0.0055 0.0061 0.0073 0.0094 0.0119 0.0168 0.0222 0.0293 0.0307]';
ZeroDates = datemnth(Settle,[6 12*[1 2 3 4 5 7 10 20 30]]');
myRC = intenvset('Rates',ZeroRates,'StartDate',Settle,'EndDates',ZeroDates,...
'Basis',3,'Compounding',1);
% Bond information
CouponRate = {{'15-Jun-2025' .02;'15-Jun-2040' .03}};
Maturity = datenum('15-Jun-2040');
Price = 90;
ExerciseDates = [datenum('15-Jun-2034') datenum('15-Jun-2035') datenum('15-Jun-2036')];
Strikes = 100;
Period = 1;
% Build HW tree
AlphaHW = .1;
VolHW = .01;
myVolSpec = hwvolspec(Settle,Maturity,VolHW,Maturity,AlphaHW);
myTimeSpec = hwtimespec(Settle,cfdates(Settle,Maturity,Period),Period);
myHWTree = hwtree(myVolSpec,myRC,myTimeSpec);
% Compute OAS
[OAS,OAD,OAC] = oasbyhw(myHWTree,Price,CouponRate,Settle,Maturity,'call',Strikes,ExerciseDates,'Period')

Best Answer

Related Solutions

MATLAB: What is the difference between IMPVBYBLS and BLSIMPV, and how to I determine the Black-Scholes implied volatility using these functions

MATLAB: How the oasbyhw function supports for stepped coupon bonds

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