How can I create a random walk (with certain probability) for stock price movement in python?

Question

I want to simulate stock price movements in Python, for 3 years, with a total of 300 steps, with 5 paths. The share price can go up or down with probability of increase = q and probability of falling = 1-q.

If it increases, the price in period t = period price t-1 x u If it decreases, the period price t = period price t-1 x d

I am kind of confused about how to use random numbers in answering this problem. While what I made like this, it can show results but I am not sure if comparing the random number with q is the right way to do this.

#m = time step
#T = year
#sigma = volatility
#S0 = price period 0
#r = riskfree
def price_path(m,T,sigma,s0,r):
    prices = np.zeros(m)
    prices[0] = s0
    u = np.exp(sigma*np.sqrt(T/m))
    d = 1/u
    q = (np.exp(sigma*T/m) - d) / (u-d)
    for i in range(m-1):
        rand_var = np.random.rand()
        if(rand_var < q):
            prices[i+1] = prices[i] * u
        else:
            prices[i+1] = prices[i] * d
    return prices

np.random.seed(3912)
fig, ax =plt.subplots()
for i  in range(5):
    rd_walk = price_path(m=300,T=3,sigma=0.25,s0=50,r=0.05)`
    plt.plot(rd_walk)

Answer 1

You have done it correctly because it is just a Bernoulli distribution.

By using numpy, you can write price_path more concisely:

def price_path(m,T,sigma,s0,r):
    
    u = np.exp(sigma*np.sqrt(T/m))
    d = 1/u
    q = (np.exp(sigma*T/m) - d) / (u-d)
    
    up_or_down = np.where(np.random.rand(m)<q,u,d)
    up_or_down[0] = 1.
    prices = s0 * np.cumprod(up_or_down)
    
    return prices