<aside> ℹ️ About
This post will help you understand the Black-Scholes equation in a conceptual way. No calculus or mathematical derivations.
It assumes you are somewhat familiar with it as a model to price options.
Why did I Write This?
I watched a video that combined with my prior understanding of the model to yield a more satisfying grasp of the intuition than the one I used to carry with me. Maybe my current grasp will resonate with readers in ways that extend their own intuition.
Here’s the video that prompted the post:
https://www.youtube.com/watch?v=bx9WvasBrxw&list=PL4108D90CA93915EB&index=14&ab_channel=BionicTurtle
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<aside> 📌 Conceptual Overview
Nobody takes the model seriously as way to compute the absolute value of an option. It is used more as a thermometer to measure what the market might be saying about implied volatility. In that sense, it’s useful for comparison.
But the intuition is a great demonstration of the replication approach that characterizes arbitrage pricing techniques. The gist of the approach rests on a simple idea:
If you can replicate the cash flow of an asset with a strategy then the price of the asset should equal the cost of executing the strategy.
If the strategy and the asset have the same cash flows, then a portfolio that is short the asset and long the strategy has no risk.
If the asset trades for a higher price than the cost to execute the strategy, then:
short the asset and execute the strategy to capture the excess cash flow
This would be a riskless profit. Since the competition for riskless profits is ruthless we can infer that the price of asset would trade in line with replication costs.
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<aside> 👽 Decomposing Black Scholes
To bring this to life, let’s set up an example to refer to.
Pricing a European-style call option with the following terms:
You can solve the formula with an online calculator, programming it into Excel or the language of your choice. Back in 2000, I programmed it into one of these:
Ok, here’s the output:
The call option is worth $7.20
It has about a .40 delta
It has about a 29% chance of expiring in-the-money
We’ll refer back to this.
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