Trade duration risk in subdiffusive financial models

Abstract

Subdiffusive processes are employed in finance to explicitly accommodate in return models the presence of random waiting times between price innovations, often referred to as “trade duration”. In this paper we argue that pricing models based on subdiffusions naturally account for the presence of a trade duration market price of risk. In particular we make a case for tempered subdiffusive models, which are able to capture the time multiscale properties of equity prices, that is, the fact that different return idleness patterns are shown at different time scales. We explain the role in duration risk pricing of the stability and tempering parameters of a tempered subdiffusion, and show that option valuation can be performed using standard integral representations.