To The Moon

 The Black-Scholes model was devised in 1973 by Fisher Black and Myron Scholes. Robert Merton helped edit the original paper written by Black and Scholes, and wrote his own paper about their model.

The Black Scholes model made a few assumptions. Options can not be exercised before expiration (European Style). There is normal distribution, meaning we wouldn’t see a “Volatility Skew”. There is no dividend. They also didn’t figure in transaction costs (commissions). Commissions in US markets have gone to zero in the past few years, and institutional traders do not pay commissions for their proprietary trading, so that assumption is now true,

There are a few models that tweak the Black-Scholes model. William Sharpe had tweaked Black Scholes in 1978. The Cox-Rubinstein (Cox-Ross-Rubinstein) model came out in late 1979. Cox-Rubinstein is sometimes called a binomial option pricing model. This model is the one most used by brokerage firms. There are a few other models.

All models use similar assumptions.

• Price of the underlying
• Call or Put
• Expiration
• Strike Price
• Interest rates
• Implied Volatility

I tested six different option pricing models a few years ago. Using the same inputs from the list above, the outcomes of a 60-day At-The-Money option that should trade around $4 was within $0.04.

The bottom line: It doesn’t matter which model your broker uses.

P.S. Fisher Black passed away in 1995. Scholes and Miller won the Nobel Prize in Economics in 1997 for the Black-Scholes model. They do not award any prize posthumously, but Black was prominently mentioned.

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