# -*- coding: utf-8 -*-
"""
Copyright Gabriel Turinici 2022
Do not distribute
Implements price and delta computation for Black - Scholes vanilla options
"""

import numpy as np
from scipy.stats import norm

def blsprice(Price,Strike,Rate,TimeToMaturity,Volatility,DividendRate=0):
    """input:
       S:Price - Current price of the underlying asset.
    
       Strike:Strike - Strike (i.e., exercise) price of the option.
    
       Rate: Rate - Annualized continuously compounded risk-free rate of return over
         the life of the option, expressed as a positive decimal number.
    
       TimeToMaturity:Time - Time to expiration of the option, expressed in years.
    
      Volatility: volatility
      DividendRate = continuous dividend rate
    """
    
    if TimeToMaturity <= 1e-6: # the option already expired
        call = np.max(Price-Strike,0)
        put = np.max(Strike-Price,0)
        return call,put
        
    
    d1 = np.log(Price/Strike)+(Rate-DividendRate + Volatility**2/2.0)*TimeToMaturity;
    d1 = d1/(Volatility* np.sqrt(TimeToMaturity))
    d2 = d1-(Volatility*np.sqrt(TimeToMaturity))
    
    call = Price * np.exp(-DividendRate*TimeToMaturity) * norm.cdf(d1)-Strike* np.exp(-Rate*TimeToMaturity) * norm.cdf(d2)
    put  = Strike* np.exp(-Rate*TimeToMaturity) * norm.cdf(-d2)-Price* np.exp(-DividendRate*TimeToMaturity) * norm.cdf(-d1)
    return call,put

#test: blsprice(100,110,0.05,1,0.2)
#blsprice(np.array([100,101]),np.array([110,111]),0.05,1,0.2)

def blsdelta(Price,Strike,Rate,TimeToMaturity,Volatility,DividendRate=0):
    """input:
       S:Price - Current price of the underlying asset.
    
       Strike:Strike - Strike (i.e., exercise) price of the option.
    
       Rate: Rate - Annualized continuously compounded risk-free rate of return over
         the life of the option, expressed as a positive decimal number.
    
       TimeToMaturity:Time - Time to expiration of the option, expressed in years.
    
      Volatility: volatility
      DividendRate = continuous dividend rate
    """
    
    if TimeToMaturity <= 1e-6: # the option already expired
        call = (Price>=Strike).astype(np.float) # 1 if in the money, zero otherwise
        put = (Price<=Strike).astype(np.float) # cf above
        return call,put
        
    
    d1 = np.log(Price/Strike)+(Rate-DividendRate + Volatility**2/2.0)*TimeToMaturity;
    d1 = d1/(Volatility* np.sqrt(TimeToMaturity))
    
    call =  np.exp(-DividendRate*TimeToMaturity) * norm.cdf(d1)
    put  = -np.exp(-DividendRate*TimeToMaturity) * norm.cdf(-d1)
    return call,put