The Black-Scholes model reduces to a known physics equation solvable by hand

Evidence

The models described in the chapters that follow are the outcomes of analytical thinking, of the manipulation of equations, and sometimes of geometric reasoning. They are underpinned by sophisticated economic thinking, and sometimes by advanced mathematics, but computationally they are not overwhelmingly complex. The Black-Scholes-Merton model of option pricing, for example, yields as its central result a differential equation (the “Black-Scholes equation” equation 1 in appendix D) that has no immediately obvious solution but is nevertheless a version of the “heat” or “diffusion” equation, which is well known to physicists. After some tinkering, Black and Scholes found that in the case of options of the most basic kind the solution of their equation is a relatively simple mathematical expression (equation 2 in appendix D). The numerical values of the solution can be calculated by hand using standard mathematical tables. — Donald MacKenzie, An Engine, Not a Camera, 41

Categorization

• XREF: Black-Scholes being a diffusion/heat equation ties to broader literature on how finance borrowed physics techniques; connects to Mirowski’s cyborg sciences frame already flagged in ch. 2. — connects to: The arbitrage argument produces the Black-Scholes partial differential equation. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95; The Black-Scholes equation is a version of the physicists’ heat equation. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 41; Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 584

Broader Connections

• The Black-Scholes equation is a version of the physicists’ heat equation. #corroborates (0.95) — Donald MacKenzie, An Engine, Not a Camera, 41
• Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation #expands (0.72) — Donald MacKenzie, An Engine, Not a Camera, 584
• The arbitrage argument produces the Black-Scholes partial differential equation. #qualifies (0.70) — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95