来自 numpy Monte Carlo 投资模拟的错误结果 returns

Question

How much money will you get by investing ,000 periodically at an average rate of 8% annually for 30 years and using monte carlo simulations?

我正在尝试通过对 python 中的利率使用 Monte Carlo 模拟来解决上述问题。我想出了下面的代码，它似乎是正确的，但它非常歪斜，我怀疑我做错了什么。下面代码

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt

def sni(i,n):
    sni = round(((1+i)**n-1)/i,2)
    return sni

df = pd.DataFrame()
investment = 10000
for p in range(1000):
    i = np.random.normal(0.08,0.18)
    lst = []
    for n in range(30):
        final = investment * sni(i,n)
        lst.append(final)
    df[p]=lst

Answer 1

我不记得我袖手旁观的方程式，但我怀疑你无论如何都有多年来的利率变化，所以这个指数的东西是行不通的。

然后我就这样做了：

import numpy as np
import pylab

years = 30
investment = 10000.0

def one_run():
    account = 0
    for n in range(years):
        interest = np.random.normal(0.08, 0.018)
        account = account * (1 + interest) + investment
    return account

df = [one_run() for _ in range(10000)]
    
# ****** everything below here is just plotting

p, b = np.histogram(df,50, density=True)
pylab.plot(b[:-1], p)
pylab.grid()
pylab.xlabel("Return [$]")
pylab.ylabel("Probability density [1/$]")
pylab.show()

此外，您将利率以 0.18 的比例在 0.08 左右变化，即很多时候它会是负数。我自由地在此处插入另一个零（值为 0.08 +- 0.018）。

来自 numpy Monte Carlo 投资模拟的错误结果 returns

Incorrect results from a numpy Monte Carlo simulation of investment returns

python

simulation

finance

numpy

montecarlo