Description
StochDedication.gms: Stochastic Dedication model. Consiglio, Nielsen and Zenios. PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 6.2.1 Last modified: Apr 2008.
Category : GAMS FIN library
Mainfile : StochDedication.gms includes : BondData.inc SpotRates.inc FactorData.inc
$TITLE Stochastic Dedication model
* StochDedication.gms: Stochastic Dedication model.
* Consiglio, Nielsen and Zenios.
* PRACTICAL FINANCIAL OPTIMIZATION: A Library of GAMS Models, Section 6.2.1
* Last modified: Apr 2008.
SETS
Time Time periods /2001 * 2011/
Scenarios Set of scenarios /SS_1 * SS_9/;
ALIAS (Scenarios, l, ll);
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/;
SET
Factors Term structure factors
/FF_1, FF_2, FF_3/;
ALIAS(Factors, j);
ALIAS(Bonds, i);
PARAMETERS
Price(i) Bond prices
Coupon(i) Coupons
Maturity(i) Maturities
Liability(t) Stream of liabilities
F(t,i) Cashflows;
* Bond data. Prices, coupons and maturities from the Danish market
$INCLUDE "BondData.inc"
$INCLUDE "FactorData.inc"
PARAMETER
beta(j,t) Factor loadings;
* Transpose factor loadings
beta(j,t) = betaTrans(t,j);
* Copy/transform data. Note division by 100 to get unit data, and
* subtraction of "Now" from Maturity date (so consistent with tau):
Price(i) = BondData(i,"Price")/100;
Coupon(i) = BondData(i,"Coupon")/100;
Maturity(i) = BondData(i,"Maturity") - Now;
* Calculate the ex-coupon cashflow of Bond i in year t:
F(t,i) = 1$(tau(t) = Maturity(i))
+ coupon(i) $ (tau(t) <= Maturity(i) AND tau(t) > 0);
PARAMETER
Liability(t) Liabilities
/2002 = 80000, 2003 = 100000, 2004 = 110000, 2005 = 120000,
2006 = 140000, 2007 = 120000, 2008 = 90000, 2009 = 50000,
2010 = 75000, 2011 = 150000/;
* Read spot rates
PARAMETER r(t)
/
$ONDELIM
$INCLUDE "SpotRates.inc"
$OFFDELIM
/;
* Generate spot rate scenarios, Sr(t,s), using factors from FactorData.inc .
PARAMETER
Sr(t,l) Spot rate scenarios;
PARAMETER
FactorWeights(j,l) Weights of each factor under each scenario
/FF_1.SS_1 0.01, FF_1.SS_2 -0.02, FF_1.SS_3 0.04,
FF_2.SS_4 0.02, FF_2.SS_5 0.01, FF_2.SS_6 0.01,
FF_3.SS_7 -0.01, FF_3.SS_8 -0.01, FF_3.SS_9 -0.02/;
Sr(t,l)$(r(t) <> 0) = r(t) + SUM(j, FactorWeights(j, l) * beta(j,t));
PARAMETERS
pr(l) Scenario probability
/SS_1 = 10, SS_2 = 5, SS_3 = 11,
SS_4 = 2, SS_5 = 7, SS_6 = 9,
SS_7 = 15, SS_8 = 3, SS_9 = 3/;
* Scale probabilities to one.
pr(l) = pr(l) / SUM(ll, pr(ll));
DISPLAY pr, Sr;
* Calculate the scenario-dependent present values for both
* bonds and liabilities.
PARAMETERS
P(i) Implied market price
PV(i,l) Bonds present value
PVL(l) Liabilities present value;
PV(i,l) = SUM(t, F(t,i) * exp(-Sr(t,l) * tau(t)));
PVL(l) = SUM(t, Liability(t) * exp(-Sr(t,l) * tau(t)));
P(i) = SUM(l, pr(l) * PV(i,l) );
DISPLAY PV, PVL;
SCALARS
Budget Initial budget /800000/
Omega Bound on the expected shortfalls /1275/;
POSITIVE VARIABLES
yPos(l) Positive deviations
yNeg(l) Negative deviations
x(i) Holdings of assets in monetary units (not proportions);
VARIABLE
z Objective function value;
EQUATIONS
BudgetCon Equation defining the budget contraint
ObjDef Objective function definition
TargetDevDef(l) Equations defining the positive and negative deviations
PutCon Constraint to bound the expected value of the negative deviations ;
ObjDef .. z =e= SUM(l, pr(l) * yPos(l));
BudgetCon .. SUM(i, P(i) * x(i)) =E= Budget;
PutCon .. SUM(l, pr(l) * yNeg(l)) =L= Omega;
TargetDevDef(l) .. SUM(i, PV(i,l) * x(i)) =E= PVL(l) + yPos(l) - yNeg(l);
MODEL StochDedication 'PFO Model 6.4.1' /ALL/;
SOLVE StochDedication MAXIMIZING z USING LP;
DISPLAY x.l;