期权二叉树python代码

以下是一个简单的期权二叉树的 Python 代码示例：

import math

class OptionTreeNode:
    def __init__(self, underlying, strike, time_to_expiry, risk_free_rate, volatility):
        self.underlying = underlying
        self.strike = strike
        self.time_to_expiry = time_to_expiry
        self.risk_free_rate = risk_free_rate
        self.volatility = volatility
        self.up = None
        self.down = None
        self.option_value = 0

def build_option_tree(underlying, strike, time_to_expiry, risk_free_rate, volatility, steps):
    dt = time_to_expiry / steps
    discount_factor = math.exp(-risk_free_rate * dt)
    up_factor = math.exp(volatility * math.sqrt(dt))
    down_factor = 1 / up_factor

    root = OptionTreeNode(underlying, strike, time_to_expiry, risk_free_rate, volatility)
    current_layer = [root]

    for i in range(steps):
        next_layer = []
        for node in current_layer:
            node.up = OptionTreeNode(node.underlying * up_factor, strike, node.time_to_expiry - dt, risk_free_rate, volatility)
            node.down = OptionTreeNode(node.underlying * down_factor, strike, node.time_to_expiry - dt, risk_free_rate, volatility)
            next_layer.append(node.up)
            next_layer.append(node.down)
        current_layer = next_layer

    for node in current_layer:
        node.option_value = max(node.underlying - node.strike, 0)

    for i in range(steps-1, -1, -1):
        current_layer = []
        for j in range(i):
            node = OptionTreeNode(0, strike, 0, risk_free_rate, volatility)
            node.up = current_layer[j]
            node.down = current_layer[j+1]
            node.option_value = discount_factor * (node.up.option_value + node.down.option_value) / 2
            current_layer.append(node)
        current_layer.reverse()

    return root

def calculate_option_price(underlying, strike, time_to_expiry, risk_free_rate, volatility, steps):
    root = build_option_tree(underlying, strike, time_to_expiry, risk_free_rate, volatility, steps)
    return root.option_value

# 示例用法
underlying_price = 100
strike_price = 110
expiry_time = 1
risk_free_rate = 0.05
volatility = 0.2
steps = 100

option_price = calculate_option_price(underlying_price, strike_price, expiry_time, risk_free_rate, volatility, steps)
print("期权价格为:", option_price)

这段代码实现了一个简单的期权二叉树模型，可以计算欧式期权的价格。其中，`build_option_tree` 函数用于构建期权二叉树，`calculate_option_price` 函数用于计算期权价格。在示例中，我们假设标的资产价格为100，执行价为110，到期时间为1年，无风险利率为5%，波动率为20%，模拟步数为100步。最终输出的是期权的价格。

请注意，这只是一个简单的示例代码，没有考虑真实市场的复杂情况和各类期权的特殊性质。在实际使用中，可能需要根据具体需求进行更复杂的扩展和调整。