Year
2025
Client
Me, i still need projects.
Category
Finance \\ Python
Product Duration
1 Week
The Black-Scholes-Merton (BSM) model is a mathematical model used to calculate the theoretical price of European-style options. Developed by Fischer Black, Myron Scholes, and Robert Merton, it revolutionized financial markets by providing a closed-form solution for option pricing.
Core Concepts:
Purpose: Computes fair prices for European call and put options, helping traders and investors make informed decisions.
Inputs:
Current price of the underlying asset
Strike price of the option
Time to maturity (in years)
Volatility of the underlying asset (annualized standard deviation)
Risk-free interest rate (annualized, continuous compounding)
Outputs: The model provides the theoretical price for both call and put options, as well as sensitivities like delta and gamma.
Assumptions:
The underlying asset follows a geometric Brownian motion with constant volatility and drift.
No dividends are paid during the life of the option.
Markets are frictionless (no transaction costs or taxes).
The risk-free rate and volatility are constant.
The option can only be exercised at expiration (European style).
Practical Use:
The BSM model is widely used in financial markets for pricing, risk management, and strategy development.
It also provides "Greeks" (sensitivities) like delta and gamma, which are crucial for hedging and risk assessment
Technologies
Streamlit: (web application framework)NumPy: (numerical computations)Pandas: (data manipulation)SciPy: (statistical functions, e.g., normal CDF)Matplotlib: (data visualization)Seaborn: (statistical data visualization)Plotly: (interactive plots)



