The Black Scholes Model: How Ed Thorp Made It Cool

“When the interests of the salesmen and promoters differ from those of the client, the client had better look out for himself.”

The Black-Scholes Model is a nobel prize winning math model that simulates the dynamics of a financial market’s derivatives (including options, futures and swaps). Thorp first introduced the model in 1973, and after working out some kinks in its infancy, the model quickly became revered as the standard for estimating options prices. The vital idea surrounding the model is to hedge the options in an investment portfolio by buying and selling the underlying stock outright and as a result— eliminating risk.

Using the same amalgam of principles he used to bust the Vegas casinos, Thorp’s model assumes the price of high volume assets follow a (cue the big-brain-speak) “geometric brownian motion” with constant volatility. When applied to an option, the model implements the constant price variation of the stock and the greeks for each contract.

Initially the model is based on the core assumption that the market has at least one risky ticker floating in the ether and another risk-free asset, like cash or bonds. In addition, it assumes three properties of the two assets, and four of the market itself.

The black scholes assumptions include:

1. The option is european and can only be exercised at expiration.

2. No dividends are paid out during the options lifetime.

3. Markets are efficient.

4. There are no negative carry costs.

5. The risk free rate and volatility of the contract are known and constant.

6. The returns on the stock are normally distributed.

If you’ve read any Taleb, you’ve likely heard him reference lognormal distribution, or more famously, “gaussian distribution”. The black- scholes model assumes a stocks price follow this lognormal distribution as an asset price can’t go negative, and are known to have significant right skewness in your risk analyzer. This is known as a “fat tail”; we’ll delve deeper into that in another post.