The Search for a Black-Scholes of Prediction Markets

TLDR:

- Options only took off once Black-Scholes gave traders a shared model for pricing risk.

- Prediction markets lack that: no universal way to structure probabilities, hedge event risk, or map uncertainty.

- A probability surface could be the missing piece.

1. How Options Found Liquidity

Before 1973, options were opaque and illiquid. Pricing was guesswork.

Black, Scholes, and Merton published a model that gave traders a common language.

Black-Scholes introduced:
(1) Implied volatility
(2) Dynamic hedging
(3) A replicable pricing framework

The assumptions were unrealistic, but it did not matter. A shared kernel was enough.

Liquidity exploded and the ecosystem evolved into:
- Volatility surfaces
- Stochastic volatility models
- Jump-diffusion processes
- Exotic derivatives

Options became one of the world’s deepest markets.

2. Prediction Markets Today

Similar to options pre-1973: visible but fragmented.

There's no universal framework to:
- Adjust probabilities
- Hedge risk
- Structure uncertainty

Current problems:
- Liquidity fragmented
- Spreads wide on niche events
- Market makers face uncharted risks

Platforms experiment with LMSR, constant-product AMMs, and order books, but these are execution mechanisms, not pricing models.

What is missing is a shared formula to map how probabilities behave across time and conditions.

3. Toward a Probability Surface

Options use the volatility surface to map risk.

Prediction markets could develop an analogue: the probability surface.

Key dimensions:
- Time to resolution, similar to option maturity
- Conditionality, similar to strike dependence (e.g., “Trump wins presidency” linked to “Republicans win Senate”)
- Belief volatility, when odds swing from 40% to 70% to 50%. That variance itself could be tradable

Possible products:
- Volatility swaps on belief
- Structured products on conditional outcomes

The goal is to show not just single-point odds but the full shape of uncertainty across time and related events.

4. Why It Matters

Without a model, markets remain fragmented and shallow.

With a model, prediction markets could scale into an institutional asset class.

Benefits include:
- Market makers quoting consistently, deepening liquidity
- Traders hedging exposure like in FX or commodities
- New products such as correlation trades across events, variance swaps on probabilities, and structured products tied to conditional paths

Black-Scholes was wrong in key ways, but it unlocked an ecosystem.

Prediction markets need the same. Not perfection, just the first widely adopted model.

5. The Open Question

Who will create the “Black-Scholes” of prediction markets?

The formula that turns event contracts from curiosities into the foundation of a trillion-dollar asset class.