Do LLMs Quote Arbitrage-Free Option Prices? A Multi-Model Internal-Consistency Probe

We test whether an LLM’s own option surface respects the deterministic static no-arbitrage invariants. A table can parse cleanly and still violate model-free relations. This violation is a measurable internal-consistency failure that is separate from pricing accuracy. The probe ran 225 fixed-seed generation attempts at temperature 0, spread over 5 smoke-tested text endpoints and five prompt families. Of these, 223 parsed. At the predeclared 1% spot-scaled tolerance, 90.58% of the parsed surfaces violated at least one invariant; the required DeepSeek baseline, taken alone, had 82.22% AVR. The audited object is the model’s own quoted European call-put surface, scored against five static no-arbitrage relations: put-call parity, the elementary bounds, strike monotonicity, convexity in strike, and calendar monotonicity on the call leg. A deterministic validator runs after the parser. Any surface whose worst residual exceeds the predeclared tolerance is failed.