Description
Dedication.gms: Dedication model without borrowing. Consiglio, Nielsen and Zenios. PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 2.4 Last modified: Apr 2008.
Category : GAMS FIN library
Mainfile : DedicationNoBorrow.gms includes : BondData.inc
$title Dedication model without borrowing
* Dedication.gms: Dedication model without borrowing.
* Consiglio, Nielsen and Zenios.
* PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 2.4
* Last modified: Apr 2008.
SET Time Time periods /2001 * 2011/;
ALIAS (Time, t, t1, t2);
SCALARS
Now Current year
Horizon End of the Horizon;
Now = 2001;
Horizon = CARD(t)-1;
PARAMETER
tau(t) Time in years;
* Note: time starts from 0
tau(t) = ORD(t)-1;
SET Bonds Bonds universe
/DS-8-06, DS-8-03, DS-7-07,
DS-7-04, DS-6-11, DS-6-09,
DS-6-02, DS-5-05, DS-5-03, DS-4-02
/;
ALIAS(Bonds, i);
PARAMETERS
Price(i) Bond prices
Coupon(i) Coupons
Maturity(i) Maturities
Liability(t) Stream of liabilities
rf(t) Reinvestment rates
F(t, i) Cashflows;
* Bond data. Prices, coupons and maturities from the Danish market
$include "BondData.inc"
* Copy/transform data. Note division by 100 to get unit data, and
* subtraction of "Now" from Maturity date (so consistent with tau):
Price(i) = BondData(i,"Price")/100;
Coupon(i) = BondData(i,"Coupon")/100;
Maturity(i) = BondData(i,"Maturity") - Now;
* Calculate the ex-coupon cashflow of Bond i in year t:
F(t,i) = 1$(tau(t) = Maturity(i))
+ coupon(i) $ (tau(t) <= Maturity(i) AND tau(t) > 0);
* For simplicity, we set the short term rate to be 0.03 in each period
rf(t) = 0.04;
PARAMETER
Liability(t) Liabilities
/2002 = 80000, 2003 = 100000, 2004 = 110000, 2005 = 120000,
2006 = 140000, 2007 = 120000, 2008 = 90000, 2009 = 50000,
2010 = 75000, 2011 = 150000/;
OPTION Liability:0;
DISPLAY BondData,F,Liability;
POSITIVE VARIABLES
x(i) Face value purchased
surplus(t) Amount of money reinvested;
VARIABLE
v0 Upfront investment;
EQUATION
CashFlowCon(t) Equations defining the cashflow balance;
CashFlowCon(t).. SUM(i, F(t,i) * x(i) ) +
(v0 - SUM(i, Price(i) * x(i))) $(tau(t) = 0) +
(( 1 + rf(t-1) ) * surplus(t-1)) $(tau(t) > 0) =E=
surplus(t) + Liability(t) $(tau(t) > 0);
MODEL Dedication 'PFO Model 4.2.3' /CashFlowCon/;
SOLVE Dedication MINIMIZING v0 USING LP;
DISPLAY v0.L,x.L,surplus.L,x.M,CashFlowCon.M;