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| R2012a Documentation → Financial Derivatives Toolbox | |
Learn more about Financial Derivatives Toolbox |
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| Contents | Index |
[Price, PriceTree] = bkprice(BKTree,
InstSet, Options)
BKTree | Interest-rate tree structure created by bktree. |
InstSet | Variable containing a collection of NINST instruments. Instruments are categorized by type. Each type can have different data fields. The stored data field is a row vector or string for each instrument. |
Options | (Optional) Derivatives pricing options structure created with derivset. |
[Price, PriceTree] = bkprice(BKTree, InstSet, Options) computes arbitrage-free prices for instruments using an interest-rate tree created with bktree. All instruments contained in a financial instrument variable, InstSet, are priced.
Price is a number of instruments (NINST)-by-1 vector of prices for each instrument. The prices are computed by backward dynamic programming on the interest-rate tree. If an instrument cannot be priced, NaN is returned.
PriceTree is a MATLAB structure of trees containing vectors of instrument prices and accrued interest, and a vector of observation times for each node.
PriceTree.PTree contains the clean prices.
PriceTree.AITree contains the accrued interest.
PriceTree.tObs contains the observation times.
bkprice handles instrument types: 'Bond', 'CashFlow', 'OptBond', 'OptEmBond', 'Fixed', 'Float', 'Cap', 'Floor', 'RangeFloat', 'Swap'. See instadd to construct defined types.
Related single-type pricing functions are:
bondbybk: Price a bond from a Black-Karasinski tree.
capbybk: Price a cap from a Black-Karasinski tree.
cfbybk: Price an arbitrary set of cash flows from a Black-Karasinski tree.
fixedbybk: Price a fixed-rate note from a Black-Karasinski tree.
floatbybk: Price a floating-rate note from a Black-Karasinski tree.
floorbybk: Price a floor from a Black-Karasinski tree.
optbndbybk: Price a bond option from a Black-Karasinski tree.
optembndbybk: Price a bond with embedded option by a Black-Karasinski tree.
rangefloatbybk: Price range floating note from a Black-Karasinski tree.
swapbybk: Price a swap from a Black-Karasinski tree.
swaptionbybk: Price a swaption from a Black-Karasinski tree.
Load the BK tree and instruments from the data file deriv.mat. Price the cap and bond instruments contained in the instrument set.
load deriv.mat;
BKSubSet = instselect(BKInstSet,'Type', {'Bond', 'Cap'});
instdisp(BKSubSet)
%Table of instrument portfolio partially displayed:
Index Type CouponRate Settle Maturity Period ... Name ...
1 Bond 0.03 01-Jan-2004 01-Jan-2007 1 ... 3% bond
2 Bond 0.03 01-Jan-2004 01-Jan-2008 2 ... 3% bond
Index Type Strike Settle Maturity CapReset ... Name ...
3 Cap 0.04 01-Jan-2004 01-Jan-2008 1 ... 4% Cap
[Price, PriceTree] = bkprice(BKTree, BKSubSet);
Price =
98.1096
95.6734
2.2706
You can use treeviewer to see the prices of these three instruments along the price tree.
treeviewer(PriceTree, BKSubSet)
 |
Price the following multi-stepped coupon bonds using the following data:
% The data for the interest rate term structure is as follows:
Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = 'Jan-1-2010';
StartDates = ValuationDate;
EndDates = {'Jan-1-2011'; 'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'};
Compounding = 1;
% Create RateSpec
RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);
% Create a portfolio of stepped coupon bonds with different maturities
Settle = '01-Jan-2010';
Maturity = {'01-Jan-2011';'01-Jan-2012';'01-Jan-2013';'01-Jan-2014'};
CouponRate = {{'01-Jan-2011' .042;'01-Jan-2012' .05; '01-Jan-2013' .06; '01-Jan-2014' .07}};
ISet = instbond(CouponRate, Settle, Maturity, 1);
instdisp(ISet)
%Table of instrument portfolio partially displayed:
Index Type CouponRate Settle Maturity Period Basis EndMonthRule ... Face
1 Bond [Cell] 01-Jan-2010 01-Jan-2011 1 0 1 ... 100
2 Bond [Cell] 01-Jan-2010 01-Jan-2012 1 0 1 ... 100
3 Bond [Cell] 01-Jan-2010 01-Jan-2013 1 0 1 ... 100
4 Bond [Cell] 01-Jan-2010 01-Jan-2014 1 0 1 ... 100
% Build the tree with the following data
VolDates = ['1-Jan-2011'; '1-Jan-2012'; '1-Jan-2013'; '1-Jan-2014'];
VolCurve = 0.01;
AlphaDates = '01-01-2014';
AlphaCurve = 0.1;
BKVolSpec = bkvolspec(RS.ValuationDate, VolDates, VolCurve,...
AlphaDates, AlphaCurve);
BKTimeSpec = bktimespec(RS.ValuationDate, VolDates, Compounding);
BKT = bktree(BKVolSpec, RS, BKTimeSpec);
% Compute the price of the stepped coupon bonds
PBK = bkprice(BKT, ISet)
PBK = bkprice(BKT, ISet)
%Table of instrument portfolio partially displayed:
Index Type CouponRate Settle Maturity Period Basis EndMonthRule ... Face
1 Bond [Cell] 01-Jan-2010 01-Jan-2011 1 0 1 ... 100
2 Bond [Cell] 01-Jan-2010 01-Jan-2012 1 0 1 ... 100
3 Bond [Cell] 01-Jan-2010 01-Jan-2013 1 0 1 ... 100
4 Bond [Cell] 01-Jan-2010 01-Jan-2014 1 0 1 ... 100
PBK =
100.6763
100.7368
100.9266
101.0115 |
|
Price a portfolio of stepped callable bonds and stepped vanilla bonds using the following data:
% The data for the interest rate term structure is as follows:
Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = 'Jan-1-2010';
StartDates = ValuationDate;
EndDates = {'Jan-1-2011'; 'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'};
Compounding = 1;
%Create RateSpec
RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);
% Create an instrument portfolio of 3 stepped callable bonds and three
% stepped vanilla bonds
Settle = '01-Jan-2010';
Maturity = {'01-Jan-2012';'01-Jan-2013';'01-Jan-2014'};
CouponRate = {{'01-Jan-2011' .042;'01-Jan-2012' .05; '01-Jan-2013' .06; '01-Jan-2014' .07}};
OptSpec='call';
Strike=100;
ExerciseDates='01-Jan-2011'; %Callable in one year
% Bonds with embedded option
ISet = instoptembnd(CouponRate, Settle, Maturity, OptSpec, Strike,...
ExerciseDates, 'Period', 1);
% Vanilla bonds
ISet = instbond(ISet, CouponRate, Settle, Maturity, 1);
% Display the instrument portfolio
instdisp(ISet)
%Table of instrument portfolio partially displayed:
Index Type CouponRate Settle Maturity OptSpec Strike ExerciseDates ... AmericanOpt
1 OptEmBond [Cell] 01-Jan-2010 01-Jan-2012 call 100 01-Jan-2011 ... 0
2 OptEmBond [Cell] 01-Jan-2010 01-Jan-2013 call 100 01-Jan-2011 ... 0
3 OptEmBond [Cell] 01-Jan-2010 01-Jan-2014 call 100 01-Jan-2011 ... 0
Index Type CouponRate Settle Maturity Period Basis EndMonthRule ... Face
4 Bond [Cell] 01-Jan-2010 01-Jan-2012 1 0 1 ... 100
5 Bond [Cell] 01-Jan-2010 01-Jan-2013 1 0 1 ... 100
6 Bond [Cell] 01-Jan-2010 01-Jan-2014 1 0 1 ... 100
% Build the tree with the following data
VolDates = ['1-Jan-2011'; '1-Jan-2012'; '1-Jan-2013'; '1-Jan-2014'];
VolCurve = 0.01;
AlphaDates = '01-01-2014';
AlphaCurve = 0.1;
BKVolSpec = bkvolspec(RS.ValuationDate, VolDates, VolCurve,...
AlphaDates, AlphaCurve);
BKTimeSpec = bktimespec(RS.ValuationDate, VolDates, Compounding);
BKT = bktree(BKVolSpec, RS, BKTimeSpec);
% The first three rows corresponds to the price of the stepped callable bonds
% and the last three rows corresponds to the price of the stepped vanilla bonds.
PBK = bkprice(BKT, ISet)
PBK =
100.6735
100.6763
100.6763
100.7368
100.9266
101.0115 |
|
Compute the price of a portfolio using the following data:
% The data for the interest rate term structure is as follows:
Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = 'Jan-1-2011';
StartDates = ValuationDate;
EndDates = {'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'; 'Jan-1-2015'};
Compounding = 1;
% Create RateSpec
RS = intenvset('ValuationDate', ValuationDate, 'StartDates',...
StartDates, 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding);
% Create an instrument portfolio with two range notes and a floating rate
% note with the following data:
Spread = 200;
Settle = 'Jan-1-2011';
Maturity = 'Jan-1-2014';
% First Range Note:
RateSched(1).Dates = {'Jan-1-2012'; 'Jan-1-2013' ; 'Jan-1-2014'};
RateSched(1).Rates = [0.045 0.055; 0.0525 0.0675; 0.06 0.08];
% Second Range Note:
RateSched(2).Dates = {'Jan-1-2012'; 'Jan-1-2013' ; 'Jan-1-2014'};
RateSched(2).Rates = [0.048 0.059; 0.055 0.068 ; 0.07 0.09];
% Create InstSet
InstSet = instadd('RangeFloat', Spread, Settle, Maturity, RateSched);
% Add a floating-rate note
InstSet = instadd(InstSet, 'Float', Spread, Settle, Maturity);
% Display the portfolio instrument
instdisp(InstSet)
Index Type Spread Settle Maturity RateSched FloatReset Basis Principal EndMonthRule
1 RangeFloat 200 01-Jan-2011 01-Jan-2014 [Struct] 1 0 100 1
2 RangeFloat 200 01-Jan-2011 01-Jan-2014 [Struct] 1 0 100 1
Index Type Spread Settle Maturity FloatReset Basis Principal EndMonthRule
3 Float 200 01-Jan-2011 01-Jan-2014 1 0 100 1
% The data to build the tree is as follows:
VolDates = ['1-Jan-2012'; '1-Jan-2013'; '1-Jan-2014';'1-Jan-2015'];
VolCurve = 0.01;
AlphaDates = '01-01-2015';
AlphaCurve = 0.1;
BKVS = bkvolspec(RS.ValuationDate, VolDates, VolCurve,...
AlphaDates, AlphaCurve);
BKTS = bktimespec(RS.ValuationDate, VolDates, Compounding);
BKT = bktree(BKVS, RS, BKTS);
% Price the portfolio
Price = bkprice(BKT, InstSet)
Price =
105.5147
101.4740
105.5147 |
bksens | bktree | instadd | intenvprice | intenvsens
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