Option Pricing — Black-Scholes

Description

Visualizes the Black-Scholes option pricing model through three key concepts: geometric Brownian motion stock paths, the call option payoff diagram at expiry (max(S-K, 0)), and the probability cone expanding over time. Shows how volatility sigma affects option price and presents the full Black-Scholes formula.

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Phases

#	Phase Name	Duration	Description
1	Title	3s	Show title
2	GBM Paths	10s	Animate multiple random stock price paths fanning out over time
3	Probability Cone	6s	Show the expanding cone of uncertainty around the mean path
4	Payoff Diagram	9s	Draw call option payoff at expiry: flat at 0 then rising above strike K
5	Black-Scholes Formula	7s	Display and explain C = S0N(d1) - Ke^(-rT)*N(d2)
6	Volatility Effect	9s	Show two option price curves: low sigma vs high sigma, higher sigma = higher price

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Layout

+-----------------------------------------------+
|      Option Pricing — Black-Scholes           |
|                                                |
|  Stock Paths:     ^                            |
|                   |  /--high vol              |
|                   | /                         |
|                   |/ -- mean path             |
|                    \                          |
|                     \--low vol                |
|                   +-----------> Time          |
|                                                |
|  Call Payoff:  profit                         |
|                  |          /                 |
|                  |_________/ K  St            |
|                                                |
|  C = S₀N(d₁) - Ke^{-rT}N(d₂)               |
+-----------------------------------------------+

Area Descriptions

• Top: Title
• Left: GBM random paths simulation (animated)
• Right: Probability cone
• Lower-left: Call option payoff diagram
• Bottom: Black-Scholes formula and volatility effect comparison

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Assets & Dependencies

• Fonts: LaTeX / sans-serif
• Manim version: ManimCE 0.19.1

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Notes

• GBM paths: multiple thin colored lines fan out from left
• Probability cone: shaded region growing wider over time
• Payoff diagram: axes with hockey-stick shape in gold
• Formula highlighted in gold
• Background: dark navy #1a1a2e