Using BSM model in the international currencies market with Monte Carlo simulations

[WMD]

Monte Carlo Simulations

Following Python program computes the answer to the question given in the aforesaid link.

import numpy as np
import math

# Parameters
S0 = 1.3  # Spot rate (€/£)
sigma = 0.22  # Volatility
r_GBP = 0.035  # Pound risk-free rate
r_EUR = 0.095  # Euro risk-free rate
T = 0.5  # Time to maturity (years)
num_simulations = 10000

# Generate random numbers
Z = np.random.standard_normal(num_simulations)

# Simulate future exchange rates
S_T = S0 * np.exp((r_EUR - r_GBP - 0.5 * sigma**2) * T + sigma * np.sqrt(T) * Z)

# Calculate payments in Euros
Payment_EUR = np.maximum(10 / S_T, 13)

# Discount payments to present value
Present_Value_EUR = Payment_EUR * np.exp(-r_EUR * T)

# Calculate average present value
present_value = np.mean(Present_Value_EUR)

print(f"Estimated Present Value of the Contingent Claim: {present_value:.4f} EUR")

Estimated Present Value of the Contingent Claim: 12.3970 EUR

Is formula used in the aforesaid video for computing value of the contingent claim correct?

Now, which answer is correct? The answer given in the video or the answer generated by this Python program?