Estimating unknown arbitrage costs: evidence from a three-regime threshold vector error correction model

We present a methodology for estimating a 3-regime threshold vector error correction model (TVECM) with an unknown cointegrating vector based on a new dynamic grid evaluation. This model is particularly suited to estimating deviations from parity conditions such as unknown arbitrage costs in markets with a persistent non-zero basis between two similar financial market instruments traded in the spot and the derivative markets. Our proposed 3-regime TVECM can estimate the area where arbitrageurs have no incentives for trading. Only when the basis exceeds a critical threshold, where the potential gain from the basis trade exceeds the overall transaction costs, do we expect arbitrageurs to step in and carry out the respective trade. This leads to non-linear adjustment dynamics and regimes with different characteristics. The overall transaction costs for the basis trades can be inferred from the estimated no-arbitrage regime. Our methodology allows us to quantify overall transaction costs for an arbitrage trade in markets where trading costs are opaque or unknown, as in credit risk or index arbitrage trading. The key contributions of this paper are the further development of the 2-threshold VECM, together with the numerical evaluation of the model through numerous simulations to prove its robustness. We present two short applications of the model in arbitrage trades in the palladium market and index trading for the S&P 500.