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Option Pricing — Black-Scholes

受眾: University類別: Economics

簡介

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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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.

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

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

Assets & Dependencies

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

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
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