Why Does the Black-Scholes Model Remain so Popular?

The Black-Scholes model was developed by Fischer Black and Myron Scholes in 1973 and later refined by Robert Merton.

It was the first arbitrage free model relating the option price to the hedging strategy consisting of buying or selling the underlying asset to eliminate the risk.

It is well known that some of the assumptions of the model are not empirically valid, particularly the fact that it assumes a constant volatility of the underlying asset price which it is not true in practice. But it is actually its simplicity and its elegance which may explain the popularity of the model.

The Black-Scholes model uses only one unobservable variable, the asset price volatility, to price European vanilla options.

And the Black-Scholes formula allows to translate option prices into implied volatilities, with a one-to-one relationship. There is one unique volatility implied by the price of an option and vice versa.

It is more convenient for traders to quote options in terms of implied volatilities rather than option prices. It remains more stable when the underlying price, or the time to maturity changes. It is a bit like yields for bonds. And the Black-Scholes implied volatility became quickly the market standard to quote vanilla options.

Similarly to the yield term structure implied by the prices of bonds issued by the same issuer with different time to maturity, with an additional dimension there is a volatility surface implied by option prices on the same underlying asset with different strike prices and expiry dates.

Moreover, the volatility is directly related to the risk of the underlying asset. It corresponds to the second moment, the standard deviation of log return distribution, making the implied volatility a measure which can be directly compared to the realised volatility of the underlying asset price.

Black-Scholes sensitivities, or Greeks, such as Delta, Vega, Rho, Theta, Gamma, Vanna or Volga, all available with closed-form formulas are market standards to measure and manage the risks of an option portfolio.

Even if more advanced models are often required to price and risk manage complex products or to model the volatility surface and its dynamic, the Black-Scholes model remains one of the foundation of modern quantitative finance, and it is key for all quants or aspiring quants to master it.

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