Option pricing under the Merton model of the short rate in subdiffusive Brownian motion regime

Abstract

In this paper, we propose an extension of the Merton short rate model, which reflects the subdiffusive nature of the short rate dynamics. The subdiffusive property is manifested by the random periods of time, during which the asset price does not change. We derive explicit formulas for European call and put options and present some simulation results for the case of α stable. Moreover, we discuss the implied volatility of this model.