Black Scholes Volatility and Price calculation

black_scholes_volatility.py

from math import * 

# Cumulative standard normal distribution
def cdf(x):
    return (1.0 + erf(x / sqrt(2.0))) / 2.0

# Call Price based on Black Scholes Model
# Parameters
#   underlying_price: Price of underlying asset
#   exercise_price: Exercise price of the option
#   time_in_years: Time to expiration in years (ie. 33 days to expiration is 33/365)
#   risk_free_rate: Risk free rate (ie. 2% is 0.02)
#   volatility: Volatility percentage (ie. 30% volatility is 0.30)
def black_scholes_call(underlying_price, exercise_price, time_in_years, risk_free_rate, volatility):
    d1 = (log(underlying_price / exercise_price) + risk_free_rate * time_in_years) / (volatility * sqrt(time_in_years)) + 0.5 * volatility * sqrt(time_in_years)
    d2 = d1 - (volatility * sqrt(time_in_years))
    
    return underlying_price * cdf(d1) - exercise_price * exp(-time_in_years * risk_free_rate) * cdf(d2)

# Put Price based on Black Scholes Model
# Parameters
#   underlying_price: Price of underlying asset
#   exercise_price: Exercise price of the option
#   time_in_years: Time to expiration in years (ie. 33 days to expiration is 33/365)
#   risk_free_rate: Risk free rate (ie. 2% is 0.02)
#   volatility: Volatility percentage (ie. 30% volatility is 0.30)
def black_scholes_put(underlying_price, exercise_price, time_in_years, risk_free_rate, volatility):
    return black_scholes_call(underlying_price, exercise_price, time_in_years, risk_free_rate, volatility) + exercise_price * exp(-risk_free_rate * time_in_years) - underlying_price

# Call Implied Volatility
# Parameters
#   underlying_price: Price of underlying asset
#   exercise_price: Exercise price of the option
#   time_in_years: Time to expiration in years (ie. 33 days to expiration is 33/365)
#   risk_free_rate: Risk free rate (ie. 2% is 0.02)
#   option_price: It is the market price of the option
def	implied_volatility_call(underlying_price, exercise_price, time_in_years, risk_free_rate, option_price):
    high = 5
    low = 0
    
    while (high - low) > 0.0001:
        if black_scholes_call(underlying_price, exercise_price, time_in_years, risk_free_rate, (high + low) / 2) > option_price:
            high = (high + low) / 2
        else:
            low = (high + low) / 2
    
    return (high + low) / 2

# Put Implied Volatility
# Parameters
#   underlying_price: Price of underlying asset
#   exercise_price: Exercise price of the option
#   time_in_years: Time to expiration in years (ie. 33 days to expiration is 33/365)
#   risk_free_rate: Risk free rate (ie. 2% is 0.02)
#   option_price: It is the market price of the option
def	implied_volatility_put(underlying_price, exercise_price, time_in_years, risk_free_rate, option_price):
    high = 5
    low = 0
    
    while (high - low) > 0.0001:
        if black_scholes_put(underlying_price, exercise_price, time_in_years, risk_free_rate, (high + low) / 2) > option_price:
            high = (high + low) / 2
        else:
            low = (high + low) / 2
    
    return (high + low) / 2