Estimating unknown arbitrage costs: evidence from a 3-regime threshold vector error correction model

Abstract

We present a methodology for estimating a multivariate 3-regime threshold vector error correction model (TVECM) with an unknown cointegrating vector based on a new dynamic grid evaluation. This model is particularly useful for 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 derivative markets. Our proposed 3-regime TVECM can estimate the area where arbitrageurs have no incentives to trade. It is only when the basis exceeds a critical threshold, that is when the potential gain from the basis trade exceeds the overall transaction costs, that we expect arbitrageurs to step in and carry out the respective trade. This leads to non-linear adjustment dynamics and regimes with different characteristics. Our methodology allows overall transaction costs to be quantified in markets where trading costs are opaque or unknown.