Distribution of Trading Activity across Strike Prices in the DAX Index Options Market

In this paper we propose and estimate an econometric model for the distribution of trading activity across options written on the DAX index. The model is based on the observation that in this market options with strike prices ending on 000, 200, 400, 600 and 800 (the class of 200-strike options) are more traded than options with strike prices ending on 100, 300, 500, 700 and 900 (the class of 100-strike contracts). We assume that market participants who would like to trade a continuum of contracts have to choose between the options listed by the exchange. When they have to choose between two neighboring 200- and 100-strike contracts, they prefer the 200-strike contract if the degree of substitution between these two options is high. We derive an equation which links the trading volumes of the 200- and 100-strike options and the degree of substitution between them. This equation has convenient analytical properties and can be readily estimated from the data. The estimation results confirm the hypothesised effect of the degree of substitution on the distribution of trading between 200- and 100-strike contracts. Additionally, we are able to derive some quantitative estimates of the percentage of trades attracted to the 200-strike contracts.