kozai_monte_carlo.py

import kozai.compute as kc

cluster = kc.create_dask_cluster()
dask_client = cluster.client()

print(dask_client)

import dask.bag as db
import numpy as np
from dask.distributed import Client, progress

def random_walk(s0, mu, sigma, days):
    dt = 1/365.
    prices = np.zeros(days)
    shocks = np.zeros(days)
    prices[0] = s0
    for i in range(1, days):
        e = np.random.normal(loc=mu * dt, scale=sigma * np.sqrt(dt))
        prices[i] = prices[i-1] * (1 + e)
    return prices

s0 = 100
K = 100
mu = 0.02
sigma = 0.2
days = 365*4
n = 10000

try:
    result = db \
        .from_sequence(range(0, n), npartitions=int(n / 100)) \
        .map(lambda _: max(
            0,
            np.average(random_walk(s0, mu, sigma, days)) - K
        )) \
        .to_dataframe(columns=['max']) \
        ['max'].mean()

    progress(result)

    print(result.compute())
finally:
    cluster.shutdown()