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

BIS Working Papers No 689
January 2018



We present a methodology for describing the economic conditions in which substantial price differences can persist for two similar financial instruments traded in the spot and derivatives markets. Arbitrageurs conduct trades that should reduce these price differences. But trades only become profitable for an arbitrageur if a critical threshold, the transaction cost, is exceeded. The existence of thresholds leads to the potential for abrupt adjustments and the tendency for prices to behave in different ways under differing conditions.


We use a new methodology for estimating unknown transaction costs in markets with frictions. When monitoring market distortions, it is important for regulators to understand these dynamics in terms of transaction costs and speed of price adjustments. We present two applications: arbitrage trading of palladium and the S&P 500 index.


We estimate transaction costs, as well as the long-run equilibrium, using a sequential grid search. We present a comprehensive simulation study to test our model's reliability. Persistent increases or jumps in transaction costs may hint at market distortions. We find that, with our methodology, the transaction costs for a negative and a positive basis trade are estimated with a very high degree of precision, suggesting that our method is reliable.



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.

JEL classification: G12, G14 and G15

Keywords: transaction cost, arbitrage, basis, threshold, regime switch, intraday, nonlinear, non-stationary, error correction