Agent-Based Model of Liquidity and Arbitrage Cost Between ETF and Stocks

In recent years, exchange-traded funds (ETFs) have been widely spread to individual investors as an easy way to diversify their investments. Some ETFs, however, are not traded with enough volume to discover an adequate price, making them difficult for individual investors to trade. Therefore, to increase the liquidity of low-liquidity ETFs, some stock exchanges have introduced an incentive scheme in which arbitrage orders are charged lower trading fees. The questions, however, of how the liquidity changes depending on arbitrage trading costs and what the mechanism is remain to be answered. Therefore, in this study I built an artificial market model, which is a kind of agent-based model, containing an ETF, two stocks, and an arbitrage trader. I then investigated the relationship between the liquidity of the ETF and the trading costs. The results showed that, because the prices of each risk asset fluctuate in their volatility, when the volatility is sufficiently greater than the cost, the arbitrage agent has more chances to make arbitrage trades. Then, when the arbitrage agent trades more, the market price differential becomes lower. In addition, lower cost increases the depth of waiting trades for the ETF, whereas the depth tendency for a stock is the opposite. Furthermore, lower cost increases the trading volume of both. Lower cost reduces the depth and increases the trading volume for a stock because orders for arbitrage trades and the waiting orders for a stock are matched.