python - 总结蒙特卡洛的场景

Question

我正在尝试对 Callpayoffs 中的值进行求和，因为它们代表基于先前路径 Assets 价格循环中生成的最后价格的 yield 。如果我运行 10 次模拟，则根据每个模拟路径(有 252 个价格点)的最后价格，应该有 10 个 Callpayoffs。不幸的是，我无法将 Callpayoffs 列表中的值相加。非常感谢任何帮助 - 下面是 print(sum(Callpayoffs)

的示例

4.620174500863143
22.762337253759725
0
51.97221078945353

基于我的代码

import numpy as np
import pandas as pd
from math import *
import matplotlib.pyplot as plt
from matplotlib import *


def Generate_asset_price(S,v,r,dt):
    return (1 + r * dt + v * sqrt(dt) * np.random.normal(0,1))


# initial values
S = 100
v = 0.2
r = 0.05
T = 1
N = 252 # number of steps 
dt = 0.00396825
simulations = 4


for x in range(simulations):
    stream = [100]
    Callpayoffs = []
    t = 0
    for n in range(N):
        s = stream[t] * Generate_asset_price(S,v,r,dt)
        stream.append(s)
        t += 1
    Callpayoffs.append(max(stream[-1] - S,0))   
    print(sum(Callpayoffs))

    plt.plot(stream)

Answer 1

您需要在 for 循环之外初始化 Cardpayoffs，并在迭代列表后调用 sum。以下应该可以解决问题:

Callpayoffs = []
for x in range(simulations):
    stream = [100]
    t = 0
    for n in range(N):
        s = stream[t] * Generate_asset_price(S,v,r,dt)
        stream.append(s)
        t += 1
    Callpayoffs.append(max(stream[-1] - S,0))   

print(sum(Callpayoffs))
plt.plot(stream)