Call Option Pricing: Black-Scholes Vs. Robinhood | By Henry Rossiter

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Call Option Pricing: Black-Scholes vs. RobinhoodHenry RossiterHenry Rossiter3 min readOct 21, 2019

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Robinhood, the wildly popular commission-free investing app, announced the arrival of options trading in December 2017.

Although many methods can be used to value options, none are more popular than one notorious model published by Fischer Black and Myron Scholes in 1973. The model, now known as Black-Scholes, yields a formula used to calculate the theoretical value of a European call or put option. According to Black-Scholes, the value of a call or put is a function of a few variables:

  • Strike price
  • Underlying asset price
  • Time until expiration
  • Asset price volatility
  • Risk free rate

Black-Scholes is designed to model European style options. Robinhood offers investors American style equity options. Fortunately, when applied to calls with reasonably short expiration periods and low risk free rates, the difference between the styles is minimal.

How efficient is Robinhood’s call option market? If one can compare the buy and sell prices of a tradeable derivative with the true value of the derivative, he or she could potentially find room for profit.

I scraped ACB (Robinhood’s most popular stock) call options expiring in two months from Robinhood. I used Black-Scholes to price the same products, using a 2% risk free rate. For each product, I plotted Robinhood’s ‘high fill buy’ price, ‘high fill sell’ price, and my calculated theoretical value.

The contracts with strike prices $3.50 and $4 give surprising results; the sell price is actually higher than the theoretical value. As the strike price increases the spread tightens. Here are similar plots for a few other popular stocks.

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