If you’ve ever tried to build a model of anything in the real world—from a financial market to the path of a dust particle—you’ve likely run into a fundamental, almost philosophical truth: models are not reality. They are simplifications, constructs we use to bridge the vast chasm between the clean, logical world of mathematics and the messy, infinitely complex, and often chaotic world we inhabit.
This isn’t a weakness; it’s a necessity. It is the very starting point for understanding one of the most famous—and famously flawed—models in all of finance: the Black-Scholes model for option pricing. To grasp why this model is both revolutionary and fundamentally “wrong,” we must first embark on a journey through physics, philosophy, and probability, discovering why no model is “true,” and why that’s the most important thing to know about any of them.
Models as Maps: The Lego Set View of Reality
Imagine a model of a molecule: a collection of colorful spheres and rigid rods. It’s a familiar image from every science textbook. Does it look like a real molecule? Not at all. At a quantum level, the reality is a cloud of probabilities, a dance of forces and fields. The plastic model is a drastic simplification.
Yet, it is incredibly useful. It captures the salient features—the atoms, the bonds between them, the fixed angles determined by valence electrons. It allows us to visualize, reason, and predict chemical behavior. It is a tool for thought.
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