Event Contract Mispricing via Options-Implied Probabilities

May 16, 2025

Researcher

Tejas Appana

Faculty Advisor

Not specified in the PDF

Overview

This project studies whether options-implied probabilities can be used to detect mispricing in Kalshi event contracts linked to year-end S&P 500 price buckets. The core idea is to compare the probabilities implied by the highly liquid SPX options market with the probabilities embedded in Kalshi’s binary event-market prices, then trade the differences through a statistical arbitrage strategy.

The project uses SPXW options chain data and Kalshi order book data from 2022 to 2024. It builds probability distributions using two main methods: a risk-neutral density approach based on the Breeden-Litzenberger framework and a Geometric Brownian Motion (GBM) approach using at-the-money implied volatility. After cleaning, smoothing, and pricing the options data, the study forms long-short portfolios of underpriced and overpriced Kalshi contracts and evaluates their performance against the S&P 500.

The overall goal is to test whether derivatives markets contain information that can systematically identify inefficiencies in prediction markets.

Key Findings

1. Market Validation.

• The project shows that Kalshi event contracts can be analyzed in a framework similar to derivative pricing because their binary payoffs resemble option-like structures.
• The SPX options market provided a useful and liquid source of information for estimating market-implied terminal probability distributions.
• Comparing Kalshi prices with options-implied probabilities revealed that prediction markets can contain persistent pricing inefficiencies, especially in specific market environments.

2. Impact of Methodology

• The Breeden-Litzenberger risk-neutral density method was the strongest approach and proved most effective in identifying mispriced contracts.
• The GBM-based model served as a simpler benchmark and produced useful directional signals, but it was less capable of capturing skew, fat tails, and volatility structure.
• A third direct heuristic approach based on option-price spreads was tested but was found to be unstable and underperformed, so it was discarded from active strategy development.
• The study also showed that careful data preprocessing, implied-volatility smoothing, and pricing adjustments were essential for building realistic probability estimates.

3. Strategy Methodology

• The strategy buys contracts when the model-implied probability suggests Kalshi is underpricing them and sells when Kalshi is overpricing them.
• The portfolio construction accounts for practical trading factors such as fees, liquidity constraints, lot sizing, order-book availability, and mark-to-market behavior.
• A lot size of 8 contracts was selected as the best balance between liquidity limitations, fee efficiency, and scalability.
• Performance was measured using annual return, volatility, Sharpe ratio, drawdowns, alpha, beta, and model-to-execution correlation.

4. Comparative Insights

• The Breeden-Litzenberger strategy performed exceptionally well in 2022, strongly outperforming the benchmark with high returns and low beta.
• In 2023, results were mixed: the strategy identified pricing discrepancies, but the main portfolio struggled in a strong bull-market environment, while some “sell-only” components worked better.
• In 2024, both strategies were weaker, mainly because of poor liquidity and missing late-year data, though the BLD version still showed controlled drawdowns.
• Overall, the strategy had low correlation to SPX and showed evidence of alpha generation, but it also experienced large swings and execution challenges.

Conclusion

This project demonstrates that option-implied probability distributions can be used to identify arbitrage opportunities in Kalshi prediction markets, especially when using a robust risk-neutral density framework. The evidence suggests that the SPX options market contains valuable information that can expose mispricing in binary event contracts.

At the same time, the project makes clear that real-world profitability depends heavily on liquidity, execution quality, data completeness, and risk management. While the concept is promising, the strategy in its current form remains a proof of concept rather than a fully optimized production system.

Future research should:

• improve risk-neutral density estimation
• include more realistic execution assumptions
• use Kalshi limit orders to reduce fees and slippage
• expand to other Kalshi asset classes such as Bitcoin or crude oil
• test shorter-dated contracts
• strengthen risk management and position-neutrality

Significance

This project is significant because it connects options markets and prediction markets in a practical arbitrage framework. It shows that information from a mature derivatives market can be used to evaluate and trade inefficiencies in a newer exchange like Kalshi.

By combining options pricing, implied volatility smoothing, probability estimation, and portfolio construction, the study provides a strong foundation for future research in cross-market arbitrage. It also highlights how emerging event markets may become more attractive as liquidity improves and product coverage expands.