Why This PDE Is Worth $1 Quadrillion (The Math Behind Finance Ep10)

One PDE built the entire derivatives market. We derive Black-Scholes two ways—delta-hedging and Feynman-Kac—and find it hiding inside AI.

In 1973, Black, Scholes, and Merton published the partial differential equation that would open a trillion-dollar derivatives market and earn the 1997 Nobel Prize in Economics. This episode derives the Black-Scholes PDE from scratch using two completely independent methods: delta-hedging (eliminating risk through a self-financing replicating portfolio) and the Feynman-Kac theorem (computing expected payoffs under the risk-neutral measure). Along the way, you'll see how boundary conditions produce the famous closed-form formula, why the PDE is secretly a relation among the Greeks, and—most surprisingly—why the same Kolmogorov backward equation powers modern diffusion models like Stable Diffusion and Sora.

0:00 The Trillion-Dollar PDE
1:03 The Replicating Portfolio
3:00 Itô Meets the Option — The Delta Hedge
5:03 The PDE Reveal
6:19 Boundary Conditions & the Closed Form
8:28 Feynman-Kac — The Parallel Universe
10:38 Greeks Preview — The PDE Is a Greek Identity
11:33 Same Math, Different World
13:32 Outro & Episode 11 Preview

📌 Series playlist: https://www.youtube.com/playlist?list=PLSjJDxqj7Cqx_Q81TYPi3vUjoR4Gt4Ysp

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🛠️ Tools used in this video:
- Animation: Manim Community Edition (Python)
- Voice: ElevenLabs AI
- Manim Starter Pack (31 ready-to-use scenes): https://axiommotion.gumroad.com/l/drhyqd

#BlackScholes #TheMathBehindFinance #MathAnimation

Видео Why This PDE Is Worth $1 Quadrillion (The Math Behind Finance Ep10) канала AxiomMotion