mc

gistfile1.txt

import numpy as np
import matplotlib.pyplot as plt

def gbm_simulation(S0, mu, sigma, dt, T, N):
    '''
    S0: initial stock price
    mu: expected return
    sigma: volatility
    dt: time step
    T: total time
    N: number of simulation steps
    '''
    # Generate the random steps
    steps = np.random.normal(loc=mu * dt, scale=sigma * np.sqrt(dt), size=(N, int(T/dt)))
    print(steps.shape)
    # Calculate the stock price path
    S = np.zeros_like(steps)
    for i in range(1, steps.shape[0]):
        S[i, :] = (steps[i]+1).cumprod(axis=0) * S0
    
    return S

# Set the parameters
S0 = 21818
mu = 0.023
sigma = 0.5898
dt = 1/365
T = 320/365
N = 1000000

# Simulate the time series
S = gbm_simulation(S0, mu, sigma, dt, T, N)

# Plot the results
plt.plot(S[1:100].T)
plt.title(f"Monte Carlo Simulation of BTC price \n vol: {sigma} start_price: {S0} rf_rate: {mu}")
plt.xlabel('Days')
plt.ylabel('BTC Price')
plt.show()

LOW = 15000
num_touches = sum([min(x)<LOW for x in S])

num_touches/N

LOW = 15000
num_touches = sum([x[-1]<LOW for x in S])

num_touches/N

sum([x[-1]>LOW and min(x) < LOW for x in S])/N

0.226031/(0.226031+0.322444)