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Explaining Black-Scholes to non-finance folks

This question comes up periodically now that options pricing (and related share pricing) is getting to be more rigorous. The basic question is "how do they come up with that number?" Sure, I studied this in school, but does anyone have a resource to explain it in non-technical terms so that your average employee will grasp the "why". I feel that this is at least theoretically important as we have a responsibility to inform our staff about things like stock options offered, and I get the impression that often saying "Black-Scholes" is akin to saying "I used my magic 8 ball".

Answers

Steven Weydert, MS, CFP(R)
Title: Senior Financial Analyst
Company: The Thornhill Companies
(Senior Financial Analyst, The Thornhill Companies) |

Hi Keith - the simplest explanation I've come across is here:

Yet even this 13+ minute overview requires a deep understanding of natural logs, anti-logs, standard deviation and variance, z-scores and the ability to read and interpret cumulative probability tables. If nothing else the video conveys just how difficult it is to explain the Black-Scholes-Merton option pricing model in a language people can understand.

Nevertheless, for call options (presumably what you're most interested in), the very general intuition is that an underlying stock's price can be assigned a minimum expected value (using a cumulative probability factor) and then the option's exercise price (also adjusted using a cumulative probability factor) can be subtracted from it producing an estimated option value.

For example: (Stock Price of $68 x Cumulative Probability Factor of .70) - (Exercise Price of $65 x Cumulative Probability Factor of .67) = Call Option Value of $4.05.

This is an over-simplification of what is by far the "simplest" part of the necessary calculations but it's a place to start.

Unfortunately, knowledge of the statistical concepts mentioned in the first paragraph is necessary to understand the calculation of the Cumulative Probability Factors; this is why most people simply will not be able to understand them.

Nevertheless if I had to pick one parameter to try and make sure people understand the intuition behind it's probably volatility (i.e. standard deviation and variance). Specifically, it's important to understand that assumptions regarding the future volatility of the underlying stock greatly impact the value of options - more specifically, the higher the assumed volatility, the higher the estimated value of calls (and puts for that matter).

Still, trying to explain in layman's terms the complex inter-workings of continuously compounded interest rates, the time value of money, standard deviation, z-scores and cumulative distribution curves remains an extraordinary challenge.

Topic Expert
Wayne Spivak
Title: President & CFO
Company: SBAConsulting.com
LinkedIn Profile
(President & CFO, SBAConsulting.com) |

Is there something wrong with a system so complex mathematically that not only leaves the average person clueless, but the non-average person clueless as well (unless you have a "... a deep understanding of natural logs, anti-logs, standard deviation and variance, z-scores and the ability to read and interpret cumulative probability tables."; and then hold everyone to that standard so they couldn't even begin to argue not only its merits, but possibly an application mistake?

David Howell, ASA, MBA
Title: Principal, Plante & Moran, PLLC
Company: Plante Moran, PLLC
(Principal, Plante & Moran, PLLC, Plante Moran, PLLC) |

There is a newer course on at Proformative Academy "Black Scholes Basics and Beyond" that can help explain how it works. Generally, Black Scholes is estimating the "chance" the stock price will be greater than the strike/exercise price, and by how "much", at a given point in time based on some assumptions. Its assumed no one can predict what a future stock price will be, however Black Scholes identifies a likely range of possible future prices, and the probability those could occur. However, there are other methods that can be used to do these calculations that are less of a "black box."

David

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