Correlation-Aware Pricing of Combo Contracts: A Copula-Based Approach with Out-of-Sample Validation and Quoting-Engine Evidence

Combination contracts — parlays, same-game multi-leg bets, and combo positions in prediction markets —are frequently priced under a naive independence assumption that multiplies the marginal probabilities ofeach leg. This assumption is only valid when the underlying legs are statistically independent, which is rarelytrue in practice. Using hourly and daily return data for Bitcoin (BTC) and Ethereum (ETH) as a liquid, publiclyaccessible proxy for correlated event legs, we quantify the mispricing induced by the independenceassumption, correct it using Gaussian and Student's t copula models, and validate the correction out-ofsample. We find that naive independence pricing underestimates the joint probability of a simultaneous 1%move in both assets by a factor of approximately 32, and that a t-copula model recovers the true probabilitywithin 6.5% of the empirical value, both in-sample and out-of-sample. Converting probabilities to contractprices, we show that a market maker pricing such a combo naively would lose approximately 97% ofcollected premium in expectation. Finally, we build a simplified inventory-aware quoting engine and show,via a paired experimental design across 40 independent historical windows, that copula-based quotingoutperforms naive quoting in every trial (p < 10¹¹), with a small but highly consistent per-trial P&L; advantage.We discuss the limitations of this design and directions for extension to live order-book and prediction-marketdata.