Non-tradability interval for heterogeneous rational players in the option markets

This study uses theoretical and empirical approaches to analyze a number of phenomena observed in trading floors, such as the changes in trading volumes and Bid–Ask spreads as a function of the moneyness level and the remaining time until the option’s expiration. A mathematical model for pricing options is developed that assumes two players with heterogeneous beliefs, where the objective of each player is to maximize their profit on the expiration day. By solving a system of algebraic equations, which takes into consideration the subjective beliefs of the players regarding the price of the underlying asset on expiration day, a feasible price domain is constructed that defines the boundaries within which a transaction may be executed. The developed model is applied to the special case in which the distribution of the underlying asset price on expiration day is uniform, and a sensitivity analysis for selected parameters is presented. An interesting theoretical result that emerges from the proposed model is the existence of an interval under which there is no tradability near the expiration day. The existence of this interval offers an explanation for the decrease in the apparent trading volumes of out-of-money (OTM) options, together with an increase in Bid–Ask spreads, as the expiration day approaches. The main parameters that affect the point of time after which there will be no trading are those that represent the players’ subjective beliefs about the distribution of the expiration values, and the cost of trading.