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Visual deck · 10 scenes · 24 animation beats
Black-Scholes, visually
Payoff, time value, the five inputs, the hedge, then the live explainer where you drag volatility and watch the option value curve move. The formula decoded, a worked number and implied volatility.
By Sitraka Forler · Lecturer, Durham Business SchoolUpdated 3 October 2026 About this site
The Black-Scholes formula looks like a wall of symbols. Drawn, it is one curve: the value of a call as a function of today's share price, sitting above the hockey-stick payoff. The gap between the two is time value, and the whole deck is about what makes that gap bigger or smaller.
Scene six is the live explainer from the glossary embedded full screen. Drag the volatility slider and the curve lifts; shorten the time to expiry and it melts down onto the payoff. After that the formula is read term by term, a number is worked by hand, and implied volatility is introduced as the formula run backwards.
How to drive it
- Click or tap anywhere, or press Space or the right arrow: one press is one animation beat, so you can narrate between reveals.
- Left arrow or right click goes back one beat. Escape leaves the deck.
- The position is kept in the address bar (#scene.beat), so a link lands on the exact beat you were showing.
The 10 scenes
- 1The payoff of a call at expiry: the hockey stick
- 2Before expiry the option is worth more: time value
- 3The five inputs: S, K, T, σ and r
- 4The hedge: a share and a loan that replicate the option
- 5Why no-arbitrage pins the price
- 6The live explainer: drag σ and T
- 7The formula, decoded: N(d1) and N(d2)
- 8A worked number, step by step
- 9Implied volatility: the formula run backwards
- 10What the model assumes, and where it bends