Please write a python code for this question, this question requires knowledge from both programming and finance.

Assume the following parameters for the Black-Scholes-Merton (1973) stock price model (Geometric Brownian motion): S0 = 90, initial price sigma = 0.25, volatility (percent in digits) r = 0.04, constant short rate T = 4/12, time horizon (in year fractions) ST, future price (log-normally distributed) Use M = 30 (number of points to generate on each path) Investor buys a 3-month European call (c1) with a strike price of $70 and sells a 3-month European call (c2) with a strike price of $80. Show the following: 1. Generate 1000 paths for the stock price and plot the first 50 paths. 2. Plot the histogram of the final stock prices, use 30 bins. Use plt.axvline to show the mean of the prices. 3. Compute the Monte Carlo estimator for c1, denote it by C1_0. 4. Chart showing the histogram of the call (c1) option prices. Use plt.axvline to show the mean of the prices. 5. Compute the Monte Carlo estimator for the price c2, denote it by C2_0 6. Chart showing the histogram of the call (c2) option prices. Use plt.axvline to show the mean of the prices. 7. Write a function to compute the Black Scholes call option price. Arguments of the function are S0, sigma, r, T, K. 8. Compute the Black Scholes price for c1 and c2. How do they compare with the estimated prices via Monte Carlo Simulation?