Exploring Greeks – Delta (Δ) with Python
Delta vs Stock Price import numpy as np import pandas as pd import matplotlib.pyplot as plt from scipy.stats import norm # Black-Scholes model for calculating option price and delta def…
Comprehensive Guide to Option Greeks: Insights and Applications
In mathematical finance, the Greeks serve as essential measures denoting the sensitivities or derivatives of a derivative instrument's price—like an option—to alterations in one or more underlying parameters. These parameters…
Implied Volatility: Newton-Raphson and Bisection Method
Newton-Raphson Method import numpy as np import matplotlib.pyplot as plt from scipy.stats import norm import math def bsm_option_price(S, K, T, r, sigma, option_type='call'): d1 = (math.log(S / K) + (r…
Valuing Options – Black Scholes Merton
Generate a 3D plot import numpy as np import matplotlib.pyplot as plt from mpl_toolkits.mplot3d import Axes3D from scipy.stats import norm def black_scholes_merton(S, K, T, r, sigma, option_type): d1 = (np.log(S…
Understanding BSM Theory: Analyzing Option Prices in Financial Markets
History The groundbreaking work of economists Fischer Black and Myron Scholes in 1968 laid the foundation for a significant breakthrough in financial economics. They introduced the concept of a dynamic…
Valuing Options – European and American using Binomial Pricing Model
Pricing European Put Option # Pricing European Put Option import numpy as np import matplotlib.pyplot as plt def binomial_option_pricing(S, K, T, r, sigma, n, option_type): delta_t = T / n…
Option Pay-off: Buyer and Writers
Payout for Option Buyers # Buyers Payout import numpy as np import matplotlib.pyplot as plt # Function to calculate call option payoff def call_payoff(sT, strike_price, premium): return np.where(sT > strike_price,…
The Binomial Option Pricing Method Simplified
Introduction The binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options which is based on a discrete-time framework, dividing time into a number of smaller intervals. The…
Basic Options Concepts
Options are contractual agreements that grant the holder the right, without imposing an obligation, to buy or sell a specified amount of an underlying asset at a predetermined price before…
Data Visualization and Communication for Finance – Charts
Charts play a crucial role in financial markets and are used extensively by traders, investors, and analysts to make informed decisions. Here are some of the key reasons why charts…