blackscholes.asv

介绍了kf,ekf,ukf ,pf ,upf 的程序代码

% PURPOSE : Demonstrate the differences between the following
% filters on an options pricing problem.
%           
%           1) Extended Kalman Filter  (EKF)
%           2) Unscented Kalman Filter (UKF)
%           3) Particle Filter         (PF)
%           4) PF with EKF proposal    (PFEKF)
%           5) PF with UKF proposal    (PFUKF)


% For more details refer to:

% AUTHORS  : Nando de Freitas      ([e-mail])
%            Rudolph van der Merwe ([e-mail])
%            + We re-used a bit of code by Mahesan Niranjan.             
% DATE     : 17 August 2000

clear all;
echo off;
path('./ukf',path);
path('./data',path);


% INITIALISATION AND PARAMETERS:
% ==============================
doPlot = 0;                 % 1 plot online. 0 = only plot at the end.
g1 = 3;                     % Paramater of Gamma transition prior.
g2 = 2;                     % Parameter of Gamman transition prior.
                            % Thus mean = 3/2 and var = 3/4.
T = 204;                    % Number of time steps.
R = diag([1e-5 1e-5]);      % EKF's measurement noise variance. 
Q = diag([1e-7 1e-5]);      % EKF's process noise variance.
P01 = 0.1;                  % EKF's initial variance of the
                            % interest rate.
P02 = 0.1;                  % EKF's initial variance of the volatility.

N = 10;                     % Number of particles.
optionNumber = 1;           % There are 5 pairs of options.
resamplingScheme = 1;       % The possible choices are
                            % systematic sampling (2),
                            % residual (1)
                            % and multinomial (3). 
                            % They're all O(N) algorithms. 

P01_ukf = 0.1
P02_ukf = 0.1

Q_ukf = Q;
R_ukf = R;

initr=.01
initsig=.15

Q_pfukf = 10*1e-5*eye(2);
R_pfukf = 1e-6*eye(2);
			    
alpha = 1;                     % UKF : point scaling parameter
beta  = 2;                     % UKF : scaling parameter for higher order terms of Taylor series expansion 
kappa = 1;                     % UKF : sigma point selection scaling parameter (best to leave this = 0)

no_of_experiments = 1;         % Number of times the experiment is
                               % repeated (for statistical purposes).

% DATA STRUCTURES FOR RESULTS
% ===========================

errorcTrivial = zeros(no_of_experiments,1);
errorpTrivial = errorcTrivial;
errorcPF      = errorcTrivial;
errorpPF      = errorcTrivial;
errorcPFUKF   = errorcTrivial;
errorpPFUKF   = errorcTrivial;


% LOAD THE DATA:
% =============
fprintf('\n')
fprintf('Loading the data')
fprintf('\n')
load c2925.prn;         load p2925.prn;
load c3025.prn;         load p3025.prn;
X=[2925; 3025];
[d1,i1]=sort(c2925(:,1));  Y1=c2925(i1,:);      Z1=p2925(i1,:);
[d2,i2]=sort(c3025(:,1));  Y2=c3025(i2,:);      Z2=p3025(i2,:);
d=Y1(:,1); 
% d - date to maturity.
St(1,:) = Y1(:,3)';   C(1,:) = Y1(:,2)';  P(1,:) = Z1(:,2)';
St(2,:) = Y2(:,3)';   C(2,:) = Y2(:,2)';  P(2,:) = Z2(:,2)';
% St - Stock price.
% C - Call option price.
% P - Put Option price.
% X - Strike price.
% Normalise with respect to the strike price:
for i=1:2
   Cox(i,:) = C(i,:) / X(i);
   Sox(i,:) = St(i,:) / X(i);
   Pox(i,:) = P(i,:) / X(i);
end
Cpred=zeros(T,2);
Ppred=zeros(T,2);

% PLOT THE LOADED DATA:
% ====================
figure(1)
clf;
plot(Cox');
ylabel('Call option prices','fontsize',15);
xlabel('Time to maturity','fontsize',15);
fprintf('\n')
fprintf('Press a key to continue')  
pause;
fprintf('\n')
fprintf('\n')
fprintf('Training has started')
fprintf('\n')

% SPECIFY THE INPUTS AND OUTPUTS
% ==============================
ii=optionNumber;   % Only one call price. Change 1 to 3, etc. for other prices.
X = X(ii,1);
St = Sox(ii,1:T);
C = Cox(ii,1:T);
P = Pox(ii,1:T);
counter=1:1:T;
tm = (224*ones(size(counter))-counter)/260;
u = [St' tm']';
y = [C' P']'; % Call and put prices.


% MAIN LOOP
% =========
for expr=1:no_of_experiments,

  rand('state',sum(100*clock));   % Shuffle the pack!
  randn('state',sum(100*clock));   % Shuffle the pack!  

%%%%%%%%%%%%%%%  PERFORM SEQUENTIAL MONTE CARLO  %%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%  ==============================  %%%%%%%%%%%%%%%%%%%%%

% INITIALISATION:
% ==============
xparticle_pf = ones(2,T,N);      % These are the particles for the estimate
                                 % of x. Note that there's no need to store
                                 % them for all t. We're only doing this to
                                 % show you all the nice plots at the end.
xparticlePred_pf = ones(2,T,N);    % One-step-ahead predicted values of the states.
yPred_pf = ones(2,T,N);            % One-step-ahead predicted values of y.
w = ones(T,N);                   % Importance weights.
% Initialisation:
for i=1:N,
  xparticle_pf(1,1,i) = initr; % sqrt(initr)*randn(1,1);
  xparticle_pf(2,1,i) = initsig; %sqrt(initsig)*randn(1,1);
end;
disp(' ');
 
tic;                             % Initialize timer for benchmarking

for t=2:T,    
  fprintf('PF :  t = %i / %i  \r',t,T);
  fprintf('\n')
  
  % PREDICTION STEP:
  % ================ 
  % We use the transition prior as proposal.
  for i=1:N,
    xparticlePred_pf(:,t,i) = feval('bsffun',xparticle_pf(:,t-1,i),t) + sqrtm(Q)*randn(2,1);    
  end;

  % EVALUATE IMPORTANCE WEIGHTS:
  % ============================
  % For our choice of proposal, the importance weights are give by:  
  for i=1:N,
    yPred_pf(:,t,i) = feval('bshfun',xparticlePred_pf(:,t,i),u(:,t),t);        
    lik = exp(-0.5*(y(:,t)-yPred_pf(:,t,i))'*inv(R)*(y(:,t)-yPred_pf(:,t,i)) ) + 1e-99; % Deal with ill-conditioning.
    w(t,i) = lik;    
  end;  
  w(t,:) = w(t,:)./sum(w(t,:));                % Normalise the weights.
  
  % SELECTION STEP:
  % ===============
  % Here, we give you the choice to try three different types of
  % resampling algorithms. Note that the code for these algorithms
  % applies to any problem!
  if resamplingScheme == 1
    outIndex = residualR(1:N,w(t,:)');        % Residual resampling.
  elseif resamplingScheme == 2
    outIndex = systematicR(1:N,w(t,:)');      % Systematic resampling.
  else  
    outIndex = multinomialR(1:N,w(t,:)');     % Multinomial resampling.  
  end;
  xparticle_pf(:,t,:) = xparticlePred_pf(:,t,outIndex); % Keep particles with
                                                    % resampled indices.
end;   % End of t loop.

time_pf = toc;    % How long did this take?

% Compute posterior mean predictions:
yPFmeanC=zeros(1,T);
yPFmeanP=zeros(1,T);
for t=1:T,
  yPFmeanC(t) = mean(yPred_pf(1,t,:));
  yPFmeanP(t) = mean(yPred_pf(2,t,:));  
end;  





figure(4)
clf;
domain = zeros(T,1);
range = zeros(T,1);
thex=[0:1e-3:20e-3];
hold on
ylabel('Time (t)','fontsize',15)
xlabel('r_t','fontsize',15)
zlabel('p(r_t|S_t,t_m,C_t,P_t)','fontsize',15)
for t=11:20:200,
  [range,domain]=hist(xparticle_pf(1,t,:),thex);
  waterfall(domain,t,range/sum(range));
end;
view(-30,80);
rotate3d on;
a=get(gca);
set(gca,'ygrid','off');

figure(5)
clf;
domain = zeros(T,1);
range = zeros(T,1);
thex=[0.1:1e-2:0.25];
hold on
ylabel('Time (t)','fontsize',15)
xlabel('r_t','fontsize',15)
zlabel('p(\sigma_t|S_t,t_m,C_t,P_t)','fontsize',15)