besa_gilts_test

BESA GILTS PRICING TEST FILE
R150
R157
R153
Vectorized All-in-price
Inflation Linked Bond
Inflation Linked Bond with ECPI y/y forecast

BESA GILTS PRICING TEST FILE

  The test cases are taken from the following documenentation:

  1. Bond Pricing Formulae, BESA, Quant Financial Research 1997
  2. Option Pricing for Risk Management, BESA Quant Financial Research 1998
  3. Buy/Sell Back(carries) and Forward Pricing, BESA, Quant Financial Research 1997
  4. Risk Management Methodology, BESA, Quant Financial Research 1997

clear detail

R150

detail.code{1}     = 'R150';
detail.coupon(1)   = 0.12;
detail.maturity(1) = datenum('28-Feb-2005');
detail.ldr1(1)     = datenum('31-Jan-1991');
detail.ldr2(1)     = datenum('31-Jul-1991');
detail.pay1(1)     = datenum('28-Feb-1991');
detail.pay2(1)     = datenum('31-Aug-1991');
detail.onebeforelast(1) = datenum('31-Aug-2004');
% price at YTM of 0.1455 on '30-Jun-1999'
settle_date = datenum('30-Jun-1999');
value_date = datenum(valuedate(settle_date,3));
[aip, cp, cum] = besaaip(settle_date,0.1455,detail)
%      all-in price = R94.31%,
%      cleanprice   = R90.30%,
%      cum-interest = R4.01%
%
% Modifed Durations
md = besamoddur(settle_date,0.1455,detail)
% Convexity
conv = besaconv(settle_date,0.1455,detail)
% Tenor
tenor = besatenor(value_date,detail)

aip =
   94.3105
cp =
   90.2996    4.0110   13.2891   -5.6895
cum =
  1.0e+005 *
    0.0000    0.0000    7.3018
md =
    3.7455
conv =
   19.2483
tenor =
    5.6795

R157

detail.code{2,1}    = 'R157';
detail.coupon(2,1)   = 0.135;
detail.maturity(2,1) = datenum('15-Sep-2015');
detail.ldr1(2,1)     = datenum('15-Feb-1991');
detail.ldr2(2,1)     = datenum('15-Aug-1991');
detail.pay1(2,1)     = datenum('15-Mar-1991');
detail.pay2(2,1)    = datenum('15-Sep-1991');
detail.onebeforelast(2,1) = datenum('15-Mar-2015');

R153

detail.code{3}     = 'R153';
detail.coupon(3)   =  0.13;
detail.maturity(3) = datenum('31-Aug-2010');
detail.ldr1(3) = datenum('31-Jan-1991');
detail.ldr2(3) = datenum('31-Jul-1991');
detail.pay1(3) = datenum('28-Feb-1991');
detail.pay2(3) = datenum('31-Aug-1991');
detail.onebeforelast(3) = datenum('28-Feb-2010');

Vectorized All-in-price

YTM's on 30-Jun-1999 for R150, R157 and R153 desc: TOMONTHLY: Close_Price freq: Monthly (3)

  'dates:  (1)'    'R150:  (1)'    'R153:  (1)'    'R157:  (1)'
  '30-Jun-1999'    [   14.5500]    [   15.2000]    [   15.1800]

format long
ytm = [0.1455; 0.152; 0.1518];
settle_date = datenum('30-Jun-1999')*ones(size(ytm));
value_date = datenum(valuedate(settle_date,3));
% The allinprice
[aip, cp, cum] = besaaip(settle_date,ytm,detail)

aip =
  94.31051461274338
  93.72142446449335
  92.69764169333863
cp =
  90.29955570863379   4.01095890410959  13.28910192949338  -5.68948538725662
  89.76389021791800   3.95753424657534  15.03945513861567  -6.27857553550665
  88.35243621388656   4.34520547945205  14.71379914021744  -7.30235830666138
cum =
  1.0e+005 *
   0.00001000000000   0.00000120000000   7.30179000000000
   0.00001000000000   0.00000135000000   7.30194000000000
   0.00001000000000   0.00000130000000   7.30179000000000

Inflation Linked Bond

Price R189 for settlement on the 10-October-2005 with a real yield of 2.7%

AIP R124.04813% (at 2.7%) INF AIP R165.58012% Clean Price R165.35156% Acc Inte = R0.22856% Delta = -10.1930 Modified Duration = 6.156 Duration = 6.239 Convexity = 45.347

Reference CPI on Issue date 95.6838709677419 Reference CPI on Settle date 127.71935483871 ratio 1.33480547501854

cpidetail.code      = 'R189';
cpidetail.maturity  = datenum('31-March-2013');
cpidetail.ldr1      = datenum('21-March-1999');
cpidetail.ldr2      = datenum('20-Sep-1999');
cpidetail.pay1      = datenum('31-Mar-1999');
cpidetail.pay2      = datenum('30-Sep-1999');
cpidetail.issuedate = datenum('20-Mar-2000');
cpidetail.onebeforelast = datenum('30-Sep-2012');
cpidetail.coupon    = 0.0625;
% CPI data
cpi = [95.5; 95.8; 127.6; 127.4; 128.5];
cpi_dates = datenum({'30-Nov-1999';'31-Dec-1999';'31-May-2005';'30-Jun-2005';'31-Jul-2005'});
rytm = 0.027;
ytm0 = 0.08;
settle_date = datenum('10-Oct-2005');
value_date = datenum(valuedate(settle_date,3));
% Compute the ECPI ratio
[cpi_ratio,cpi_issue,cpi_settle]=cpiratio(settle_date,cpidetail.issuedate,cpi,cpi_dates)
% pricing example
aip = besaaip(settle_date,rytm,cpidetail)
infaip = besainfaip(settle_date,rytm,cpi_ratio,cpidetail)
format short
[infaip, riskpremium, breakeven_inflation] = besainfaip(settle_date,rytm,cpi_ratio,cpidetail,ytm0)

cpi_ratio =
   1.33480547501854
cpi_issue =
  95.68387096774194
cpi_settle =
    1.277193548387097e+002
aip =
    1.240481326303094e+002
infaip =
    1.655801266007633e+002
infaip =
  165.5801
riskpremium =
 -8.9369e-004
breakeven_inflation =
    0.0516

Inflation Linked Bond with ECPI y/y forecast

User supplies new ECPI (forecast) - use the input annualize inflation rate to find cpi index where ECPI is the y/y CPI rate as an annualized percentage.

d = daysdif(cpidetail.issuedate,settle_date);
% 6% expected inflation
ecpi = 0.06;
cpi_value= ((1+ecpi)^(d/360))*cpi_issue;
cpi_ratio = cpi_value / cpi_issue;
infaip = besainfaip(settle_date,rytm,cpi_ratio,cpidetail)

infaip =
  172.3008

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