Real-time waiting-price trading interval in a heterogeneous options market: a Bernoulli distribution

Options pricing remains an open research question that is challenging for both theoreticians and practitioners. Unlike many classical binomial models that assume a “representative agent,” the model suggested herein considers two players who are heterogeneous with respect to their estimations of the distribution of the underlying asset price on expiration day, and with respect to their levels of willingness to make a transaction (eagerness level). A two-player binomial model is developed to find the real-time optimal option price in two stages. First, we determine a primary feasible pricing domain. We then find a narrower feasible domain, termed the “waiting-price trading interval,” meaning the region within which the players may either wait for better offers (due to a change in market conditions or player beliefs), or make an immediate transaction. The suggested model is formulated by a nonlinear optimization problem and the optimal price is shown to be unique. We demonstrate that the counter player's eagerness level has a significant effect on the proposed optimal option price. Using empirical analysis, several known lattice-based models for option pricing, such as CRR and Tian, are compared with the current model (herein, S-H) in which the price offered by the model player takes into account the subjective beliefs of the opposing market player. The comparison shows significant advantages to the S-H model in terms of the expected profit on expiration day.