Welcome to my GitHub profile! Here you'll find my projects and contributions related to quantitative analysis, artificial intelligence and actuarial science.
The Black-Scholes partial differential equation is:
And the solution for a European call option price c(s,t) is given by:
where
and
A model to assess financial risk using Python.
def create_life_table(age_data, mortality_rates):
"""
Create a basic life table from age data and mortality rates.
:param age_data: List of ages
:param mortality_rates: List of mortality rates corresponding to each age
:return: DataFrame containing the life table
"""
# Create an empty DataFrame
life_table = pd.DataFrame({'Age': age_data, 'Mortality Rate': mortality_rates})
# Calculate qx (probability of death between age x and x+1)
life_table['qx'] = life_table['Mortality Rate'].apply(lambda x: x / (1 + x))
# Calculate lx (number of people alive at the beginning of each age x)
life_table['lx'] = 100000 # Assuming an initial population of 100,000
life_table['lx'] = life_table['lx'].shift(1) * (1 - life_table['qx'])
life_table['lx'] = life_table['lx'].fillna(100000)
# Calculate tx (total number of person-years lived from age x onward)
life_table['tx'] = life_table['lx'].cumsum()
# Calculate ex (life expectancy at age x)
life_table['ex'] = life_table['tx'] / life_table['lx']
return life_table
# Example data
ages = list(range(0, 101)) # Ages from 0 to 100
mortality_rates = [0.01] * 100 + [0.02] # Example constant mortality rates
# Create life table
life_table_df = create_life_table(ages, mortality_rates)
print(life_table_df.head())