solutions.py

import numpy as np
import pandas as pd

def EuropeanOptionMC(forward, strike, discount_factor, time_to_maturity, volatility, number_of_samples, flag):
    standar_normal = np.random.randn(number_of_samples, 1)
    asset_at_maturity = forward * np.exp( -0.5*volatility**2*time_to_maturity + volatility*np.sqrt(time_to_maturity)*standar_normal )

    if flag == 1:
        simulated_option_price = discount_factor*(asset_at_maturity - strike).clip(0, np.inf)
    else:
        simulated_option_price = discount_factor*(strike - asset_at_maturity).clip(0, np.inf)

    return np.mean(simulated_option_price)

def ReadSwapRates(file, sheet, fromRow, numberOfRows, columnRange):
    swaprates = pd.read_excel(file, sheet_name = sheet, index_col = 0, skiprows = fromRow, usecols = columnRange)
    return swaprates[:numberOfRows]

def ExtractDatesAndMidRates(swap_rates):
    bids = np.array(swap_rates['BID'])
    asks = np.array(swap_rates['ASK'])
    return swap_rates.axes[0].tolist(), 0.5*(bids + asks)

def CalculateEmpiricalSurvivalProbabilities(number_of_samples, lambdas, last_year):
    uniforms = np.random.rand(number_of_samples, 1)
    default_years = np.floor(-1/lambdas*np.log(uniforms))
    defaults_by_year = [ np.count_nonzero(default_years == n) for n in np.arange(0, last_year )]
    return (number_of_samples - np.cumsum(defaults_by_year))/number_of_samples