Linganisha mbinu

	Mfumo wa Kuweka Bei wa Chaguo wa Black-Scholes-Merton	Nadharia ya Hisa Zinazotambulika na Muundo wa HAR
Nyanja	Fedha	Fedha
Familia	Regression model	Regression model
Mwaka wa asili	1973	2009
Mwanzilishi	Fischer Black, Myron Scholes & Robert Merton	Corsi (HAR model); Andersen, Bollerslev, Diebold & Labys (realized volatility)
Aina	Continuous-time option-pricing model	Time-series regression of realized variance
Chanzo asilia	Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637–654.	Corsi, F. (2009). A Simple Approximate Long-Memory Model of Realized Volatility. Journal of Financial Econometrics, 7(2), 174-196.
Majina mbadala	Black-Scholes formula, Black-Scholes-Merton model, BSM model, Black-Scholes opsiyon fiyatlama modeli	realized variance, HAR model, heterogeneous autoregressive model of realized volatility, HAR-RV
Zinazohusiana	4	5
Muhtasari	The Black-Scholes-Merton model, published by Fischer Black and Myron Scholes in 1973 with the theoretical framework extended by Robert Merton, gives a closed-form no-arbitrage price for European options. By assuming the underlying asset follows geometric Brownian motion with constant volatility, it derives a partial differential equation whose solution expresses the option price in terms of the stock price, strike, time to maturity, risk-free rate, and volatility — transforming option pricing from intuition into a rigorous, tractable formula.	Realized volatility estimates an asset's variance directly from high-frequency intraday returns rather than from a parametric latent process. The Heterogeneous Autoregressive (HAR) model of Corsi (2009), building on the realized-volatility framework of Andersen, Bollerslev, Diebold and Labys (2003), forecasts this measure by combining daily, weekly, and monthly volatility components, and is a strong alternative to GARCH for volatility prediction.