Black-Scholes Model Tutorials and Reference

Formulas and Calculations

Black-Scholes formulas – Explanation of Black-Scholes formulas for d1, d2, call price and put price. Step-by-step guide to calculation of option prices under the Black-Scholes model. Formulas for option Greeks (delta, gamma, theta, vega, rho).

Black-Scholes Excel implementation – Illustrates how the formulas above are implemented in Excel. Detailed guide how to create your own Black-Scholes Excel calculator for pricing of calls and puts.

Black-Scholes Excel formulas for Greeks – Second part of the above, explaining Excel implementation of Black-Scholes Greeks (delta, gamma, theta, vega, rho).

Excel Calculators

Black-Scholes Calculator – Excel calculator for call and put option prices under the Black-Scholes model.

Option Strategy Simulator – Combining the above for multiple options. Excel calculator to price option spreads and strategies using the Black-Scholes model, simulating scenarios, calculating aggregate Black-Scholes Greeks and break-even points.

Implied Volatility Calculator – Excel calculator that uses the Black-Scholes option price formulas backwards to calculate implied volatility from call or put option prices.

Black-Scholes Model Assumptions

Black-Scholes Model Assumptions – A list of assumptions taken by the model, with detailed explanation, confrontation with reality of the markets, and implications for practical use of the model.

Black-Scholes Model History

Black-Scholes Model History and Key Papers – An overview of events and earlier research that led to the Black-Scholes model, and people who played a role in the process. From Bachelier to Nobel Prize.

Original Papers by Black, Scholes, Merton

The Valuation of Option Contracts and a Test of Market Efficiency, Black-Scholes, 1972

The Pricing of Options and Corporate Liabilities, Black-Scholes, 1973

Theory of Rational Option Pricing, Merton, 1973

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