[原创]Black-Karanskl和Hull-White的Matlab三叉树实现[修正版by fantuanxiaot]

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fantuanxiaot 发表于 2015-5-6 15:01:06 |AI写论文

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原帖：https://bbs.pinggu.org/thread-3697628-1-1.html

HullWhiteTree_First的第一阶段函数也在此帖

Matlab的Hull-White三叉树实现
这个帖子的第二阶段hull-white算法有缺陷，本帖对其纠正：源码如下

本帖隐藏的内容

%% HullWhite三叉树的第二阶段
%% 第一阶段得到了初始的树
%% 第二阶段拟合当前的利率期限结构
function [FirstTree,SecondTree,ProTree,QTree]=HullWhiteTree_Second(T,N,Sigma,A,RateTerm)
%% 举例：[FirstTree,SecondTree,~,QTree]=HullWhiteTree_Second(3,3,0.01,0.1,[3.824/100 4.512/100 5.086/100])
%% [FirstTree,SecondTree,~,QTree]=HullWhiteTree_Second(3,6,0.01,0.1,[0.0343 0.03824 0.04183 4.512/100 0.04812 5.086/100])
%% [FirstTree,SecondTree,~,QTree]=HullWhiteTree_Second(4,8,0.01,0.1,[0.03 0.0343 ...
%% 0.03824 0.04183 4.512/100 0.04812 5.086/100 0.056])
%% RateTerm是利率的期限结构
%% 利率树采用连续利率
%% 先得到第一棵树
if length(RateTerm)~=N
error('Reset Your RateTerm');
end
deltaT=T/N;
MaxBin=ceil(0.184/(A*(deltaT)));
[FirstTree,ProTree,~,~]=HullWhiteTree_First(T,N,Sigma,A);
SecondTree=FirstTree;
%% 构建二期树
QTree=zeros(2*MaxBin+1,N);
Alpha=zeros(length(RateTerm),1);
for i=1:N
% 第一列
if i==1
QTree(i,1)=1;
Alpha(i)=RateTerm(i);
SecondTree(i,1)=SecondTree(i,1)+Alpha(i);
end
% 第二列
if i==2
Price=exp(-RateTerm(i)*i*deltaT);
Sum=0;
for j=1:3
Probability=ProTree{1,1};
QTree(j,i)=QTree(1,1)*Probability(j)*exp(-SecondTree(1,1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
end
Alpha(i)=(log(Sum)-log(Price))/deltaT;
SecondTree(1:3,i)=SecondTree(1:3,i)+Alpha(i);
end
% 三列以后
if i>=3
if i<=MaxBin+1
Price=exp(-RateTerm(i)*i*deltaT);
Sum=0;
for j=1:2*(i-1)+1
% 顶端
if j==1
Probability=ProTree{j,i-1};
QTree(j,i)=Probability(1)*QTree(j,i-1)*exp(-SecondTree(j,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
% 最下端
elseif j==2*(i-1)+1
Probability=ProTree{j-2,i-1};
QTree(j,i)=Probability(3)*QTree(j-2,i-1)*exp(-SecondTree(j-2,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
% 上一端
elseif j==2
Probability1=ProTree{j-1,i-1};
Probability2=ProTree{j,i-1};
QTree(j,i)=QTree(j,i)+Probability1(2)*QTree(j-1,i-1)*exp(-SecondTree(j-1,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(1)*QTree(j,i-1)*exp(-SecondTree(j,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
% 下一端
elseif j==2*(i-1)
Probability1=ProTree{j-2,i-1};
Probability2=ProTree{j-1,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-2,i-1)*exp(-SecondTree(j-2,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j-1,i-1)*exp(-SecondTree(j-1,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
else
Probability1=ProTree{j-2,i-1};
Probability2=ProTree{j-1,i-1};
Probability3=ProTree{j,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-2,i-1)*exp(-SecondTree(j-2,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j-1,i-1)*exp(-SecondTree(j-1,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability3(1)*QTree(j,i-1)*exp(-SecondTree(j,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
end
end
Alpha(i)=(log(Sum)-log(Price))/deltaT;
SecondTree(1:2*(i-1)+1,i)=SecondTree(1:2*(i-1)+1,i)+Alpha(i);
end
% 到了横列
if i>MaxBin+1
Price=exp(-RateTerm(i)*i*deltaT);
Sum=0;
for j=1:2*MaxBin+1
% 顶端
if j==1
Probability1=ProTree{j,i-1};
Probability2=ProTree{j+1,i-1};
QTree(j,i)=QTree(j,i)+Probability1(2)*QTree(j,i-1)*exp(-SecondTree(j,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(1)*QTree(j+1,i-1)*exp(-SecondTree(j+1,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
% 底端
elseif j==2*MaxBin+1
Probability1=ProTree{j-1,i-1};
Probability2=ProTree{j,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-1,i-1)*exp(-SecondTree(j-1,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j-1,i-1)*exp(-SecondTree(j-1,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
else
Probability1=ProTree{j-1,i-1};
Probability2=ProTree{j,i-1};
Probability3=ProTree{j+1,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-1,i-1)*exp(-SecondTree(j-1,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j,i-1)*exp(-SecondTree(j,i-1)*deltaT);
QTree(j,i)=QTree(j,i)+Probability3(1)*QTree(j+1,i-1)*exp(-SecondTree(j+1,i-1)*deltaT);
Sum=Sum+QTree(j,i)*exp(-SecondTree(j,i)*deltaT);
end
end
Alpha(i)=(log(Sum)-log(Price))/deltaT;
SecondTree(1:2*MaxBin+1,i)=SecondTree(1:2*MaxBin+1,i)+Alpha(i);
end
end
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

复制代码

Hull-White三叉树算法恶心死啦，但是这次结果绝对木有问题：

Black-Karanskl三叉树的实现类似于Hull-White三叉树，第一阶段根据Hull-White三叉树，第二阶段需要用数值方法求解方程，但是感觉很奇怪，有时候解方程解不出来，自己找不出问题在哪，有问题请告诉我，欢迎指正，Hull书上的结果得到了(1~3期的结果)，但是(4~6期的得不出来，书上也没有结果)。

对比一下

[FirstTree,RateTree,XTree,QTree]=BlackKarasnskiTree(3,6,0.25,0.22,[0.0343 0.03824 0.04183 4.512/100 0.04812 5.086/100])

本帖隐藏的内容

function [FirstTree,RateTree,XTree,QTree]=BlackKarasnskiTree(T,N,Sigma,A,RateTerm)
%% Black-Karasnski三叉树的实现
%% by fantuanxiaot
%% 具体可见RateTree
%% [FirstTree,RateTree,XTree,QTree]=BlackKarasnskiTree(3,6,0.25,0.22,[0.0343 0.03824 0.04183 4.512/100 0.04812 5.086/100])
%% [FirstTree,RateTree,XTree,QTree]=BlackKarasnskiTree(3,6,0.02,0.1,[0.0343 0.03824 0.04183 4.512/100 0.04812 5.086/100])
%% [FirstTree,RateTree,XTree,QTree]=BlackKarasnskiTree(3,8,0.25,0.22,...
%% [0.025 0.03 0.0343 0.03824 0.04183 4.512/100 0.04812 5.086/100])
if length(RateTerm)~=N
error('Reset Your RateTerm');
end
deltaT=T/N;
MaxBin=ceil(0.184/(A*(deltaT)));
[FirstTree,ProTree,~,~]=HullWhiteTree_First(T,N,Sigma,A);
%% 构建二期树
QTree=zeros(2*MaxBin+1,N);
RateTree=zeros(2*MaxBin+1,N);
Alpha=zeros(length(RateTerm),1);
XTree=zeros(2*MaxBin+1,N);
for i=1:N
% 第一列
if i==1
QTree(i,1)=1;
Alpha(i)=log(RateTerm(i));
XTree(1,1)=Alpha(i);
RateTree(i,1)=FirstTree(i,1)+exp(Alpha(i));
end
% 第二列
if i==2
Price=exp(-RateTerm(i)*i*deltaT);
Probability=ProTree{1,1};
QTree(1:3,i)=QTree(1,1)*Probability*exp(-exp(Alpha(i-1))*deltaT);
fun=@(alpha)(Price-sum(QTree(1:3,i).*exp(-deltaT*(exp(alpha+FirstTree(1:3,i))))));
% 求解alpha值
Alpha(i)=fsolve(fun,-3,optimset('MaxIter',200,'TolFun',1e-8));
XTree(1:3,i)=Alpha(i)+FirstTree(1:3,i);
RateTree(1:3,i)=exp(XTree(1:3,i));
end
% 三列以后
if i>=3
if i<=MaxBin+1
Price=exp(-RateTerm(i)*i*deltaT);
% 先得到Q值
for j=1:2*(i-1)+1
% 顶端
if j==1
Probability=ProTree{j,i-1};
QTree(j,i)=Probability(1)*QTree(j,i-1)*exp(-exp(Alpha(i-1)+FirstTree(1,i-1))*deltaT);
% 底端
elseif j==2*(i-1)+1
Probability=ProTree{j-2,i-1};
QTree(j,i)=Probability(3)*QTree(j-2,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-2,i-1))*deltaT);
elseif j==2
Probability1=ProTree{j-1,i-1};
Probability2=ProTree{j,i-1};
QTree(j,i)=QTree(j,i)+Probability1(2)*QTree(j-1,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-1,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(1)*QTree(j,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j,i-1))*deltaT);
elseif j==2*(i-1)
Probability1=ProTree{j-2,i-1};
Probability2=ProTree{j-1,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-2,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-2,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j-1,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-1,i-1))*deltaT);
else
Probability1=ProTree{j-2,i-1};
Probability2=ProTree{j-1,i-1};
Probability3=ProTree{j,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-2,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-2,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j-1,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-1,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability3(1)*QTree(j,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j,i-1))*deltaT);
end
end
fun=@(alpha)(Price-sum(QTree(1:2*(i-1)+1,i).*exp(-deltaT*(exp(alpha+FirstTree(1:2*(i-1)+1,i))))));
Alpha(i)=fsolve(fun,-3,optimset('MaxIter',200,'TolFun',1e-8));
XTree(1:2*(i-1)+1,i)=Alpha(i)+FirstTree(1:2*(i-1)+1,i);
RateTree(1:2*(i-1)+1,i)=exp(XTree(1:2*(i-1)+1,i));
end
% 到了横列
if i>=MaxBin+2
Price=exp(-RateTerm(i)*i*deltaT);
for j=1:2*MaxBin+1
% 顶端
if j==1
Probability1=ProTree{j,i-1};
Probability2=ProTree{j+1,i-1};
QTree(j,i)=QTree(j,i)+Probability1(2)*QTree(j,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(1)*QTree(j+1,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j+1,i-1))*deltaT);
elseif j==2*MaxBin+1
Probability1=ProTree{j-1,i-1};
Probability2=ProTree{j,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-1,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-1,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j,i-1))*deltaT);
else
Probability1=ProTree{j-1,i-1};
Probability2=ProTree{j,i-1};
Probability3=ProTree{j+1,i-1};
QTree(j,i)=QTree(j,i)+Probability1(3)*QTree(j-1,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j-1,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability2(2)*QTree(j,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j,i-1))*deltaT);
QTree(j,i)=QTree(j,i)+Probability3(1)*QTree(j+1,i-1)*exp(-exp(Alpha(i-1)+FirstTree(j+1,i-1))*deltaT);
end
end
fun=@(alpha)(Price-sum(QTree(1:2*MaxBin+1,i).*exp(-deltaT*(exp(alpha+FirstTree(1:2*MaxBin+1,i))))));
Alpha(i)=fsolve(fun,-3,optimset('MaxIter',500,'TolFun',1e-10));
XTree(1:2*MaxBin+1,i)=Alpha(i)+FirstTree(1:2*MaxBin+1,i);
RateTree(1:2*MaxBin+1,i)=exp(XTree(1:2*MaxBin+1,i));
end
end
end
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%