写一段matlab代码:通过输入s,u,d,T,N,K,r,风险中性方法或动态复制方法,欧式看涨期权、欧式看跌期权、美式看涨期权或美式看跌期权,来计算期权价格
时间: 2023-06-25 11:07:42 浏览: 155
Black 和 Scholes 公式 - 派息股票的欧式期权:此代码计算派息股票的看涨期权和看跌期权的价格-matlab开发
以下是一个示例的 Matlab 代码,用于计算期权价格:
```matlab
function [price, delta] = option_price(s, u, d, T, N, K, r, method, type, style)
% s: 股票价格
% u: 上涨幅度
% d: 下跌幅度
% T: 到期时间
% N: 时间步数
% K: 行权价
% r: 无风险利率
% method: 风险中性方法或动态复制方法
% type: 欧式看涨期权(eu_call)、欧式看跌期权(eu_put)、美式看涨期权(am_call)或美式看跌期权(am_put)
% style: 美式期权类型(只有在 type 为美式期权时才需要),0代表美式看涨期权,1代表美式看跌期权
dt = T / N; % 时间步长
p = (1 + r - d) / (u - d); % 上涨概率
% 计算股票价格树和期权价格树
s_tree = nan(N+1, N+1); % 股票价格树
v_tree = nan(N+1, N+1); % 期权价格树
s_tree(1,1) = s;
for i = 2:N+1
for j = 1:i
s_tree(i,j) = s_tree(i-1,j) * u;
s_tree(i,j+1) = s_tree(i-1,j) * d;
end
end
% 计算期权价格
if strcmpi(method, 'risk_neutral')
% 风险中性方法
q = (1-p); % 下跌概率
for j = 1:N+1
if strcmpi(type, 'eu_call')
v_tree(N+1,j) = max(0, s_tree(N+1,j) - K);
elseif strcmpi(type, 'eu_put')
v_tree(N+1,j) = max(0, K - s_tree(N+1,j));
elseif strcmpi(type, 'am_call') || strcmpi(type, 'am_put')
v_tree(N+1,j) = max(0, s_tree(N+1,j) - K);
end
end
for i = N:-1:1
for j = 1:i
if strcmpi(type, 'eu_call')
v_tree(i,j) = exp(-r*dt) * (p*v_tree(i+1,j+1) + q*v_tree(i+1,j));
elseif strcmpi(type, 'eu_put')
v_tree(i,j) = exp(-r*dt) * (p*v_tree(i+1,j+1) + q*v_tree(i+1,j));
elseif strcmpi(type, 'am_call')
v_tree(i,j) = max(s_tree(i,j) - K, exp(-r*dt) * (p*v_tree(i+1,j+1) + q*v_tree(i+1,j)));
elseif strcmpi(type, 'am_put')
v_tree(i,j) = max(K - s_tree(i,j), exp(-r*dt) * (p*v_tree(i+1,j+1) + q*v_tree(i+1,j)));
end
end
end
elseif strcmpi(method, 'dynamic_replication')
% 动态复制方法
for j = 1:N+1
if strcmpi(type, 'eu_call')
v_tree(N+1,j) = max(0, s_tree(N+1,j) - K);
elseif strcmpi(type, 'eu_put')
v_tree(N+1,j) = max(0, K - s_tree(N+1,j));
elseif strcmpi(type, 'am_call') || strcmpi(type, 'am_put')
v_tree(N+1,j) = max(0, s_tree(N+1,j) - K);
end
end
for i = N:-1:1
for j = 1:i
if strcmpi(type, 'eu_call') || strcmpi(type, 'am_call')
delta = (v_tree(i+1,j+1) - v_tree(i+1,j)) / (s_tree(i,j+1) - s_tree(i,j));
elseif strcmpi(type, 'eu_put') || strcmpi(type, 'am_put')
delta = (v_tree(i+1,j) - v_tree(i+1,j+1)) / (s_tree(i,j) - s_tree(i,j+1));
end
if strcmpi(type, 'am_call')
v_tree(i,j) = max(s_tree(i,j) - K, exp(-r*dt) * (delta*s_tree(i,j+1)+(1-delta)*s_tree(i,j)) - delta*s_tree(i,j+1));
elseif strcmpi(type, 'am_put')
v_tree(i,j) = max(K - s_tree(i,j), exp(-r*dt) * (delta*s_tree(i,j+1)+(1-delta)*s_tree(i,j)) - (1-delta)*s_tree(i,j+1));
end
end
end
end
% 返回期权价格和 delta
price = v_tree(1,1);
if strcmpi(type, 'eu_call') || strcmpi(type, 'am_call')
delta = (v_tree(2,2) - v_tree(2,1)) / (s_tree(2,2) - s_tree(2,1));
elseif strcmpi(type, 'eu_put') || strcmpi(type, 'am_put')
delta = (v_tree(2,1) - v_tree(2,2)) / (s_tree(2,1) - s_tree(2,2));
end
end
```
使用示例:
```matlab
s = 100; % 股票价格
u = 1.1; % 上涨幅度
d = 0.9; % 下跌幅度
T = 1; % 到期时间
N = 100; % 时间步数
K = 100; % 行权价
r = 0.05; % 无风险利率
method = 'risk_neutral'; % 风险中性方法或动态复制方法
type = 'eu_call'; % 欧式看涨期权(eu_call)、欧式看跌期权(eu_put)、美式看涨期权(am_call)或美式看跌期权(am_put)
style = 0; % 美式期权类型(只有在 type 为美式期权时才需要),0代表美式看涨期权,1代表美式看跌期权
% 计算期权价格
[price, delta] = option_price(s, u, d, T, N, K, r, method, type, style);
% 输出结果
fprintf('期权价格: %f\n', price);
fprintf('Delta: %f\n', delta);
```
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