Digital Options - Binary Options Pricing
Last reviewed: by Options Analysis Suite Research.
Digital Options
When to Use This Model
Best for: Analyzing prediction markets (Kalshi, Polymarket, Robinhood prediction), pricing binary yes/no outcomes, extracting implied probabilities from prices, and finding mispricings in event markets.
Market condition: Binary events with clear outcomes - elections, Fed decisions, earnings beat/miss, FDA approvals, or any yes/no question.
Example: A prediction market prices "SPY above $600 by December" at 64 cents. Digital options tell you if that's fair value or mispriced based on current volatility and time remaining.
Digital (binary) options pay a fixed amount if the underlying is above (call) or below (put) the strike at expiration, and zero otherwise. They're the mathematical foundation of prediction markets and provide a direct way to trade on probability-weighted outcomes.
What It's Used For
- Prediction Market Analysis: Fair value calculation for Kalshi, Polymarket, and other prediction platforms
- Probability Extraction: Convert option prices to implied probabilities of events
- Binary Event Pricing: Value yes/no outcomes like earnings surprises, FDA decisions, elections
- Mispricing Detection: Find edge in prediction markets by comparing model prices to market prices
- Hedging Binary Risk: Precise hedging for all-or-nothing exposures
Digital Option Parameters
| Parameter | Options | Interpretation |
|---|---|---|
| Payoff Type | Cash-or-Nothing / Asset-or-Nothing | Cash: pays fixed amount Q if ITM. Asset: pays asset value S if ITM |
| Payoff Amount | Q (typically $1 or $100) | The fixed payment received if option expires in-the-money |
| Strike | Price level | The threshold price that determines win/lose outcome |
| Option Type | Call / Put | Call: pays if S > K. Put: pays if S < K |
Our Implementation Features
- Analytical Pricing: Closed-form Black-Scholes digital formulas for cash-or-nothing and asset-or-nothing
- Probability Extraction: Direct calculation of risk-neutral probability from digital prices
- Gap Risk Adjustment: Smoothing for discrete monitoring to handle gap risk at barriers
- Full Greeks: Delta (probability density), gamma (rate of change), vega, theta
- Spread Replication: Show equivalent tight call/put spread for hedging
Key Advantages
Direct probability interpretation makes them intuitive for event trading. Foundation of prediction markets now accessible to retail. Clean binary payoff simplifies P&L analysis. Greeks have direct probability interpretations (delta = probability density at strike).
Trading with Digital Options
Prediction Market Analysis Workflow:
- Get Market Price: Prediction market shows 64 cents for "SPY > $600 by Dec 31"
- Extract Probability: Market implies 64% probability of SPY > $600
- Model Fair Value: Use current SPY price, IV, and time to price the digital call
- Compare: If model says 58 cents (58% prob), market may be overpriced by 6 cents
- Consider Edge: Account for bid-ask spread and fees before trading
Example: Kalshi contract "Fed raises rates in January" trades at $0.35. Your model using Fed funds futures and historical volatility prices it at $0.28. The $0.07 difference might represent an edge - or the market knows something your model doesn't. Digital options help you quantify and track these opportunities.
This page is part of the Options Analysis Suite documentation hub. Browse the glossary for term definitions.