swapbybk - Price swap instrument from Black-Karasinski interest-rate tree

Examples

Price Interest-Rate Swap

Price an interest-rate swap with a fixed receiving leg and a floating paying leg. Payments are made once a year, and the notional principal amount is $100. The values for the remaining arguments are:

• Coupon rate for fixed leg: 0.15 (15%)

• Spread for floating leg: 10 basis points

• Swap settlement date: Jan. 01, 2005

• Swap maturity date: Jan. 01, 2008

Based on the information above, set the required arguments and build the LegRate, LegType, and LegReset matrices:

Settle = '01-Jan-2005';
Maturity = '01-Jan-2008';
Basis = 0; 
Principal = 100;
LegRate = [0.15 10]; % [CouponRate Spread] 
LegType = [1 0]; % [Fixed Float] 
LegReset = [1 1]; % Payments once per year 

Price the swap using the BKTree included in the MAT-file deriv.mat. The BKTree structure contains the time and forward-rate information needed to price the instrument.

load deriv.mat; 

Use swapbybk to compute the price of the swap.

Price  = swapbybk(BKTree, LegRate, Settle, Maturity, LegReset,... 
Basis, Principal, LegType)

Price =

  39.1827

Using the previous data, calculate the swap rate, which is the coupon rate for the fixed leg, such that the swap price at time = 0 is zero.

LegRate = [NaN 20]; 

[Price, PriceTree, SwapRate] = swapbybk(BKTree, LegRate, ... 
Settle, Maturity, LegReset, Basis, Principal, LegType) 

Price =

     0

PriceTree = 

     FinObj: 'BKPriceTree'
       PTree: {1x5 cell}
        tObs: [0 1 2 3 4]
     Connect: {[2]  [2 3 4]  [2 2 3 4 4]}
      Probs: {[3x1 double]  [3x3 double]  [3x5 double]}
SwapRate =

    0.0438

Price an Amortizing Swap

Price an amortizing swap using the Principal input argument to define the amortization schedule.

Create the RateSpec.

Rates = 0.035;
ValuationDate = '1-Jan-2011';
StartDates = ValuationDate;
EndDates = '1-Jan-2017';
Compounding = 1;

RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)

RateSpec = 

           FinObj: 'RateSpec'
      Compounding: 1
             Disc: 0.8135
            Rates: 0.0350
         EndTimes: 6
       StartTimes: 0
         EndDates: 736696
       StartDates: 734504
    ValuationDate: 734504
            Basis: 0
     EndMonthRule: 1

Create the swap instrument using the following data:

Settle ='1-Jan-2011';
Maturity = '1-Jan-2017';
Period = 1;
Spread = 0;
LegRate = [0.04 10];

Define the swap amortizing schedule.

Principal ={{'1-Jan-2013' 100;'1-Jan-2014' 80;'1-Jan-2015' 60;'1-Jan-2016' 40; '1-Jan-2017' 20}};

Build the BK tree and assume volatility is 10%.

MatDates = {'1-Jan-2012'; '1-Jan-2013';'1-Jan-2014';'1-Jan-2015';'1-Jan-2016';'1-Jan-2017'};
BKTimeSpec = bktimespec(ValuationDate, MatDates);
Volatility = 0.10;  
AlphaDates = '01-01-2017';
AlphaCurve = 0.1;
BKVolSpec = bkvolspec(ValuationDate, MatDates, Volatility*ones(1,length(MatDates))', AlphaDates, AlphaCurve);
BKT = bktree(BKVolSpec, RateSpec, BKTimeSpec);

Compute the price of the amortizing swap.

Price = swapbybk(BKT, LegRate, Settle, Maturity, 'Principal' , Principal)

Price =

    1.4574