andreachello

for i in range(1,num_steps+1):
    # fill out the first value with our initial stock price value and firm value
    term_stock_val[i-1][0] = (np.full((num_simulations*i), S_0),np.full((num_simulations*i), S_0)) 
        
    for j in range (1,num_of_months):
        # update current month to reflect the monthly simulation we are currently in
        current_month = (j-1)/12
       
        corr_matrix = np.array([[1,correlation],[correlation,1]])
        norm_matrix = norm.rvs(size = np.array([2,num_simulations*i]))

andreachello

for i in range(1,num_steps+1):
    # fill out the first value with our initial stock price
    term_val[i-1][0] = np.full((num_simulations*i), S_0)
    
    for j in range (1,num_of_months):
        # update current month to reflect the monthly simulation we are currently in
        current_month = (j-1)/12
        norm_array = norm.rvs(size = num_simulations*i)
        term_val[i-1][j] = terminal_shareprice(term_val[i-1][j-1],risk_free,sigma,norm_array,dT)
    

andreachello

np.random.seed(0)
num_simulations = 1000
# the number of steps represent the times we simulate the process, with each step comprising
# 1000*i steps so we get simulations from 1000 to 50000
num_steps = 50
num_of_months = 13
# terminal price is an array of size 13 to account for the 12 months plus initial value
# it is timed by the number of steps
term_val = [[None]*num_of_months]*num_steps 

andreachello

def get_barrier_price(strike_num):
    for i in range(1,num_steps+1):
        # fill out the first value with our initial stock price
        term_val[i-1][0] = np.full((num_simulations*i), S_0)

        for j in range (1,num_of_months):
            # update current month to reflect the monthly simulation we are currently in
            current_month = (j-1)/12
            norm_array = norm.rvs(size = num_simulations*i)
            term_val[i-1][j] = terminal_shareprice(term_val[i-1][j-1],risk_free,sigma,norm_array,dT)

andreachello

for i in range(1,num_steps+1):
    # fill out the first value with our initial stock price
    term_val[i-1][0] = np.full((num_simulations*i), S_0)
    
    for j in range (1,num_of_months):
        # update current month to reflect the monthly simulation we are currently in
        current_month = (j-1)/12
        norm_array = norm.rvs(size = num_simulations*i)
        term_val[i-1][j] = terminal_shareprice(term_val[i-1][j-1],risk_free,sigma,norm_array,dT)
    

andreachello

np.random.seed(0)
num_simulations = 1000
# the number of steps represent the times we simulate the process, with each step comprising
# 1000*i steps so we get simulations from 1000 to 50000
num_steps = 50
num_of_months = 13
# terminal price is an array of size 13 to account for the 12 months plus initial value
# it is timed by the number of steps
term_val = [[None]*num_of_months]*num_steps 

andreachello

for i in range(1,num_steps+1):
    # fill out the first value with our initial stock price
    term_val[i-1][0] = np.full((num_simulations*i), S_0)
    
    for j in range (1,num_of_months):
        # update current month to reflect the monthly simulation we are currently in
        current_month = (j-1)/12
        norm_array = norm.rvs(size = num_simulations*i)
        term_val[i-1][j] = terminal_shareprice(term_val[i-1][j-1],risk_free,sigma,norm_array,dT)
    

andreachello

np.random.seed(0)
num_simulations = 1000
# the number of steps represent the times we simulate the process, with each step comprising
# 1000*i steps so we get simulations from 1000 to 50000
num_steps = 50
num_of_months = 13
# terminal price is an array of size 13 to account for the 12 months plus initial value
# it is timed by the number of steps
term_val = [[None]*num_of_months]*num_steps 

andreachello

def terminal_shareprice(S_0, risk_free_rate, sigma, Z, T):
    """
    Generates the terminal share price given some random normal values, z
    """
    # It returns an array of terminal stock prices.
    return S_0*np.exp((risk_free_rate-sigma**2/2)*T+sigma*np.sqrt(T)*Z)

def discounted_call_payoff(S_T, K, risk_free_rate, T):
    """
    Function for evaluating the discounted payoff of a call option

andreachello

import numpy as np
import pandas as pd
from scipy.stats import norm
import matplotlib.pyplot as plt
import math as m
import random as r

#Market information
risk_free = 0.08