Julia port of linkedin post https://www.linkedin.com/posts/tanveerbhatti_design-modelrisk-career-activity-7076318971389472768-aO_c

call-price.jl

using Random
using Statistics: mean
using BenchmarkTools

function calculate_call_price(S, K, r, sigma, T, iterations)
    """
    Calculates the price of a vanilla call option using Monte Carlo simulation
    
    Parameters:
        S (float): Initial stock price.
        K (float): Strike price.
        r (float): Risk-free interest rate.
        sigma (float): Stock price volatility.
        T (float): Time to maturity in years.
        iterations (int): Number of Monte Carlo iterations.
    
    Returns:
        float: Option price.
    """
    dt = T / 365
    drift = (r - 0.5 * sigma ^ 2) * dt
    vol = sigma * sqrt(dt)

    option_prices = []

    for _ in 1:iterations
        price_path = [S]
        for _ in 1:Int(T)
            push!(price_path, price_path[end] * exp(drift * vol * rand())) # broken
        end
        push!(option_prices, max(price_path[end] - K, 0))
    end
    return mean(option_prices) * exp(-r * T)
end

stock_price = 100.0
strike_price = 105.0
interest_rate = 0.05
volatility = 0.2
time_to_maturity = 1.0
num_iterations = 100000

# Uncomment the following 2 lines first to confirm the result it correct before benchmarking
# call_price = calculate_call_price(stock_price, strike_price, interest_rate, volatility, time_to_maturity, num_iterations)
# print("The price of the call option is: $(call_price)")

@btime calculate_call_price(stock_price, strike_price, interest_rate, volatility, time_to_maturity, num_iterations)
num_iterations = 1000000
@btime calculate_call_price(stock_price, strike_price, interest_rate, volatility, time_to_maturity, num_iterations)