binomial_tree_option_pricing.py

import scipy.stats as st
import numpy as np


def binomial_tree_pricing_model(
    option_type: str,
    s: float,
    k: float,
    r: float,
    v: float,
    q: float,
    t: float,
    n: int,
) -> float:
    """
    Parameters:
        option_type: option type, use 'call' or 'put'
        s: spot price
        k: strike price
        r: interest rate
        v: volatility
        q: yield rate
        t: maturity(year)
        n: periods
    
    
    ---
    Test1:
    binomial_tree_pricing_model(
        option_type = 'call', s = 810, k = 800, r = 0.05,
        v = 0.2, q = 0.02, t = 6/12, n = 2
     )
     
     Output:
        53.3947
        
    ---
    
    Test2:
    binomial_tree_pricing_model(
        option_type = 'put', s = 50, k = 50, r = 0.1,
        v = 0.4, q = 0, t = 5/12, n = 5
    )
    
    Output:
        4.3190
    """
    delta_t = t / n
    u = np.exp(v * np.sqrt(delta_t))
    d = np.exp(-v * np.sqrt(delta_t))
    p = (np.exp((r - q) * delta_t) - d) / (u - d)

    asset_price = [s * (u**j) * (d ** (n - j)) for j in range(n + 1)]

    if option == "call":
        option_price = [max(s - k, 0) for s in asset_price]
    elif option == "put":
        option_price = [max(k - s, 0) for s in asset_price]
    else:
        raise ValueError("Wrong option input.")

    option_tree = [[] for _ in range(n)]
    option_tree.append(option_price)

    for i in range(1, n + 1):
        last_level = option_tree[n - i + 1]

        for j in range(1, len(last_level)):
            down_price = last_level[j - 1]
            up_price = last_level[j]

            option_tree[n - i].append(
                np.exp(-r * delta_t) * (up_price * p + down_price * (1 - p))
            )

    return option_tree[0][0]