% Simplified spot rate curve extraction (coupon stripping). % % This is a simplified example from the paper: % % Analyzing the Indonesian Government Bond Market % with a New Coupon Stripping Model and Principal Components % by K. O. Kortanek and H. Yunianto % (see page 15 for the GP problem formulation) % % Performs the spot rate curve extraction (coupon stripping) from % financial data that only include bonds with no coupon payments. % This results in a GP that can be found on the page 15 of the paper. % % Almir Mutapcic 01/15/06 %******************************************************************** % problem data %******************************************************************** % problem sizes N = 2; % number of bonds (length of PVhat) L = 1; % number of uniform perturbation intervals % observed prices based on hypothetical bond data (this is made up data) PVhat = [98.85; 96.25]; % maturity for each bond (in years) T = [0.008; 0.015]; % problem constants (all made up) RH = 1; RL = .5; RHinf = 1; RLinf = .5; WH = 1; WL = .5; global beta gamma1 gamma2; beta = -0.1005; gamma1 = 0.999*ones(N,1); gamma2 = 0.999*ones(N,1); %******************************************************************** % problem variables, objective function, and constraints %******************************************************************** % GP variables gpvar x(2*L+2+1) % note: w_bar = exp(x_2*L+2+1) % objective function obj = inv(x(L+2+1)) + x(L+2+1); % model prices % denote P_k(T_k) as PV PV = posynomial; for k = 1:N PV(k,1) = 100*x(1)^ar(T(k))*x(2)^aalpha(T(k)); PV(k,1) = PV(k)*x(3)^b(T(k)); % here b is the same as aalpha end % hard constraint on r c1 = [ exp(-RH)*x(1) <= 1; exp(RL)*x(1)^(-1) <= 1]; % hard constraint on alpha/-beta c2 = [ exp(RHinf*beta)*x(2) <= 1; exp(-RLinf*beta)*x(2)^(-1) <= 1]; % "driving" constraints c_drive = [ exp(-WH)*x(3)*x(4)^-1*x(5)^-1 <= 1; exp(WL)*x(3)^-1*x(4)^-1*x(5) <= 1 ]; % constraint set constr = [ c_drive; c1; c2; PV <= PVhat ]; %******************************************************************** % solving the GP problem %******************************************************************** % extract the spot rate curve from the observables [oval sol status] = gpsolve(obj, constr); % evaluate and display computed prices disp(' ') fprintf(1,'Estimate of PV(1) is %3.4f versus observed PV_hat(1) = %3.4f.\n',... eval(PV(1), sol), PVhat(1)); fprintf(1,'Estimate of PV(2) is %3.4f versus observed PV_hat(2) = %3.4f.\n',... eval(PV(2), sol), PVhat(2));