Finance-Aware Spatiotemporal Reconstruction of Incomplete Implied Volatility Surfaces

An implied volatility surface is typically rebuilt each day from that day’s quotes alone, even though the quotes missing on a given day were usually traded the previous day. We treat a panel of daily surfaces as frames over moneyness, maturity and calendar time—a video-completion view—and reconstruct a target day’s missing region from the surrounding days. The model propagates along the three axes separately, mixes them by a gate reading which nodes are absent, and learns only a correction to a classical single-day fit. Using S&P 500 index options from January 2010 to August 2025, we score against strictly held-out market quotes. When an entire wing is withheld, the reconstruction beats a cross-sectional benchmark by 27.1%; holding the architecture fixed and varying only the input window shows that nine days of context rather than one accounts for a further 15.0% of the remaining error. Under random withholding, the method does not help, and under an interior expiry withholding it slightly hurts. Temporal information is thus valuable for structured outages, wing outages above all. The completed surface violates static no-arbitrage conditions more often than the benchmark, however, and a projection removing those violations removes most of the accuracy advantage, so it is not yet ready for pricing or risk use.