function Call_Option_Pricing_Plot(varargin)

%  copyright by fantuanxiaot

%  关注fantuanxiaot的量化分析新浪博客：http://blog.sina.com.cn/u/2029278253

%  期权定价作图的帽子图和三角图

%  Rate年无风险收益率，K是执行价格，T是到期时间(以年计量)

%  Sigma是年波动率，S是基期价格

%  N是划分的时间段数

%  基于二叉树的期权定价作图

%% Call_Option_Pricing is begin

%  参数的输入

S=varargin{1};

K=varargin{2};

T=varargin{3};

Rate=varargin{4};

Sigma=varargin{5};

N=varargin{6};

%  单期收益率

r=Rate*T/360/N;

DeltaT=T/N;

%  初始化期权价格矩阵

Call_Option_Pricing_Matrix=zeros(N+1);

%  在Q测度下的风险中性概率

U=exp(Sigma*sqrt(DeltaT));

D=1/U;

P=(exp(r*DeltaT)-D)/(U-D);

%  最后一列的期权价值

for i=1:N+1

Call_Option_Pricing_Matrix(i,N+1)=max(0,S*D^(i-1)*U^(N+1-i)-K);

end

%  期权价值向前推移

%  Call_Option_Pricing_Matrix形成了期权价格递归矩阵

for j=N:-1:1

for i=1:j

Call_Option_Pricing_Matrix(i,j)=exp(-DeltaT*r)*...

(Call_Option_Pricing_Matrix(i,j+1)*P+Call_Option_Pricing_Matrix(i+1,j+1)*(1-P));

end

end

%% Call_Option_Pricing_Hat_Plot is begin

%  期权定价的帽子作图

%  形成元胞位置矩阵:position_matrix

figure(1)

set(figure(1),'color','w')

hold on

xlim([-0.1 1.1])

ylim([-0.1 1.1])

for i=1:(N+1)

position_matrix{i,N+1}=[1 (N+1-i)/N];

end

for i=1:N

for j=1:i

position_matrix{j,i}=[(i-1)/N (i+1-j)/(i+1)];

end

end

%  形成二叉树基础图

hold on

for i=1:N

for j=1:i

position_1=[position_matrix{j,i};position_matrix{j,i+1}];

[arrowx,arrowy]=arrow_plot(gca,position_1(:,1),position_1(:,2));

annotation('textarrow',arrowx,arrowy,'headwidth',10,'color','m')

position_2=[position_matrix{j,i};position_matrix{j+1,i+1}];

[arrowx,arrowy]=arrow_plot(gca,position_2(:,1),position_2(:,2));

annotation('textarrow',arrowx,arrowy,'headwidth',10,'color','r')

end

end

hold on

%  基于Call_Option_Pricing_Matrix来标注期权价值

for i=1:(N+1)

for j=1:i

index=num2str(Call_Option_Pricing_Matrix(j,i));

pos=position_matrix{j,i};

text(pos(1),pos(2)+0.02,index,'fontsize',12,'fontname','Times New Roman');

end

end

title('欧式看涨期权定价的尖尖帽子图','fontsize',16,'fontname','楷体')

ylabel('Call Options Value','fontsize',16,'fontname','Times New Roman')

xlabel('时间分段','fontsize',16,'fontname','楷体')

hold off

%% Call_Option_Pricing_Triangle_Plot is begin

%  期权定价的三角形作图

clear position_matrix

figure(2)

set(figure(2),'color','w')

hold on

xlim([-0.1 1.1])

ylim([-0.1 1.1])

%  形成元胞位置矩阵:position_matrix

for i=1:(N+1)

position_matrix{i,N+1}=[1 (N+1-i)/N];

end

for i=1:N

high=0.5-(i-1)/N*0.5;

if i==1

delta=0;

else

delta=(1-2*high)/(i-1);

end

for j=1:i

position_matrix{j,i}=[(i-1)/N 1-high-(j-1)*delta];

end

end

%  形成二叉树基础图

hold on

for i=1:N

for j=1:i

position_1=[position_matrix{j,i};position_matrix{j,i+1}];

[arrowx,arrowy]=arrow_plot(gca,position_1(:,1),position_1(:,2));

annotation('textarrow',arrowx,arrowy,'headwidth',10,'color','g')

position_2=[position_matrix{j,i};position_matrix{j+1,i+1}];

[arrowx,arrowy]=arrow_plot(gca,position_2(:,1),position_2(:,2));

annotation('textarrow',arrowx,arrowy,'headwidth',10,'color','c')

end

end

hold on

%  基于Call_Option_Pricing_Matrix来标注期权价值

for i=1:(N+1)

for j=1:i

index=num2str(Call_Option_Pricing_Matrix(j,i));

pos=position_matrix{j,i};

text(pos(1),pos(2)+0.02,index,'fontsize',12,'fontname','Times New Roman');

end

end

title('欧式看涨期权定价的三角图','fontsize',16,'fontname','楷体')

ylabel('Call Options Value','fontsize',16,'fontname','Times New Roman')

xlabel('时间分段','fontsize',16,'fontname','楷体')

hold off

end

%  标注箭头函数

function varargout=arrow_plot(varargin)

if length(varargin{1})== 1 && ishandle(varargin{1}) && ...

strcmp(get(varargin{1},'type'),'axes')

hAx=varargin{1};

varargin=varargin(2:end);

else

hAx = gca;

end;

if length(varargin)==1

pos = varargin{1};

else

[x,y] = deal(varargin{:});

end

%%Get limits

axun = get(hAx,'Units');

set(hAx,'Units','normalized');

axpos = get(hAx,'Position');

axlim = axis(hAx);

axwidth = diff(axlim(1:2));

axheight = diff(axlim(3:4));

if exist('x','var')

varargout{1} = (x-axlim(1))*axpos(3)/axwidth + axpos(1);

varargout{2} = (y-axlim(3))*axpos(4)/axheight + axpos(2);

else

pos(1) = (pos(1)-axlim(1))/axwidth*axpos(3) + axpos(1);

pos(2) = (pos(2)-axlim(3))/axheight*axpos(4) + axpos(2);

pos(3) = pos(3)*axpos(3)/axwidth;

pos(4) = pos(4)*axpos(4)/axheight;

varargout{1} = pos;

end

set(hAx,'Units',axun)

end