convergence_plot.py

import matplotlib.pyplot as plt
from matplotlib.widgets import TextBox, Button
from pricing.binomial_method import binomial_method 
from pricing.black_scholes import black_scholes

"""
    Computes and plots the absolute pricing error between the binomial method and Black-Scholes as a function of the number of steps (N)

    """
t_0 = 0

fig, ax = plt.subplots()
plt.subplots_adjust(bottom=0.4)

ax_S = plt.axes([0.3, 0.25, 0.3, 0.05])
box_S = TextBox(ax_S, "Share Price: ", initial="100")

ax_E = plt.axes([0.3, 0.2, 0.3, 0.05])
box_E = TextBox(ax_E, "Strike Price: ", initial="105")

ax_r = plt.axes([0.3, 0.15, 0.3, 0.05])
box_r = TextBox(ax_r, "Interest Rate:", initial = "0.1")

ax_sigma = plt.axes([0.3, 0.1, 0.3, 0.05])
box_sigma = TextBox(ax_sigma, "Volatility:", initial = "0.1")

ax_T = plt.axes([0.3, 0.05, 0.3, 0.05])
box_T = TextBox(ax_T, "Expiry:", initial = "3")

def submit(event):
    S = float(box_S.text)
    E = float(box_E.text)
    r = float(box_r.text)
    sigma = float(box_sigma.text)
    T = float(box_T.text)





    _, _, bs_price, _ = black_scholes(S, E, r, sigma, T, t_0)

    print(f"The fair price for a European Vanilla Call on this asset is" ,bs_price)
    N_values = [3, 10, 25, 50, 100, 250, 500, 1000, 2000]

    binomial_prices = [binomial_method(S, E, r, sigma, T, t_0, N) for N in N_values]
    errors = [abs(bp - bs_price) for bp in binomial_prices]



    ax.clear()
    ax.plot(N_values, errors, marker='o')
    ax.set_xscale('log')
    ax.set_yscale('log')
    ax.set_xlabel('Number of steps, N')
    ax.set_ylabel('|Binomial - Black-Scholes|')
    ax.set_title('Convergence of Binomial Tree to Black-Scholes')
    ax.grid(alpha=0.3, which = 'both')
    fig.canvas.draw_idle()


ax_button = plt.axes([0.75, 0.1, 0.2, 0.06])
run_button = Button(ax_button, "Calculate")
run_button.on_clicked(submit)
plt.show()