linear-normal rising stock model

linear_normal_stochastic.py

import numpy as np
import matplotlib.pyplot as plt


# Config
n = 1000 # Compute 1000 grid points
ys = np.zeros(n + 1)
ys[0] = 25000 # $
y_fin = 32000 # $
sigma = 22 # $
t_init = 200000 # day
t_end  = 200112 # day
mu = (y_fin - ys[0]) / n # $ per time
dt = float(t_end - t_init) / n # per time
ts = np.arange(t_init, t_end + dt, dt)


# Stochastics
def dW(t):
    # This model is currently actually independent of t
    # Note: Use e.g. Levy flights for something wilder, 
    # or maybe there's something more natural in stock prices 
    return np.random.normal(loc=0.0, scale=np.sqrt(dt))


# Simulate
for i in range(1, ts.size):
    t = (i - 1) * dt
    y = ys[i - 1]
    ys[i] = y + mu * dt + sigma * dW(t)

# Plot
plt.plot(ts, ys, c="green")
plt.xlabel("day time")
plt.title("fucking Bitcoin")
h = plt.ylabel("$$$")
h.set_rotation(0)

plt.show()