#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Tue Nov 5 10:46:42 2019 @author: turinici """ 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)