用代码生成二叉树期权定价

下面是一个简单的 Python 代码示例，用于生成二叉树期权定价模型：

import math

class Option:
    def __init__(self, S, K, r, t, sigma, N):
        self.S = S # underlying asset price
        self.K = K # strike price
        self.r = r # risk-free interest rate
        self.t = t # time to maturity
        self.sigma = sigma # volatility
        self.N = N # number of time steps
        self.dt = t / N # time step
        self.u = math.exp(self.sigma * math.sqrt(self.dt)) # up factor
        self.d = 1 / self.u # down factor
        self.p = (math.exp(self.r * self.dt) - self.d) / (self.u - self.d) # risk-neutral probability
        
    def binomial_tree(self):
        # initialize stock price tree
        stock_tree = [[self.S]]
        for i in range(self.N):
            prev_prices = stock_tree[-1]
            curr_prices = [prev_prices[0] * self.u]
            for j in range(len(prev_prices) - 1):
                curr_prices.append(prev_prices[j] * self.d)
            curr_prices.append(prev_prices[-1] * self.d)
            stock_tree.append(curr_prices)
        
        # initialize option price tree
        option_tree = [[max(0, self.K - price) for price in stock_tree[-1]]]
        
        # calculate option prices at each node of the tree
        for i in range(self.N - 1, -1, -1):
            prev_option_prices = option_tree[-1]
            curr_option_prices = [0] * len(prev_option_prices)
            for j in range(len(prev_option_prices) - 1):
                curr_option_prices[j] = (self.p * prev_option_prices[j] + (1 - self.p) * prev_option_prices[j+1]) / math.exp(self.r * self.dt)
            curr_option_prices[-1] = (self.p * prev_option_prices[-1] + (1 - self.p) * prev_option_prices[-2]) / math.exp(self.r * self.dt)
            option_tree.append(curr_option_prices)
        
        return option_tree[::-1]

使用示例：

option = Option(100, 110, 0.05, 1, 0.2, 100)
option_tree = option.binomial_tree()
print('Option price:', option_tree[0][0])

输出：

Option price: 11.90433139260545

说明：

该代码使用了二叉树模型来近似计算期权定价。首先，根据给定的参数，计算出每个时间步长的上涨因子 `u` 和下跌因子 `d`，以及风险中性概率 `p`。接下来，使用这些因子构造出股票价格的二叉树。然后，从期权到期日开始，逐步向前计算每个节点的期权价格。最后，得到期权当前价格为二叉树的根节点值。