Trade Duration Risk in Subdiffusive Financial Models

12 Pages Posted: 27 Mar 2019

See all articles by Lorenzo Torricelli

Lorenzo Torricelli

University of Bologna Department of Statistics

Date Written: February 18, 2019


Subdiffusive processes can be used in finance to explicitly accommodate the presence of random waiting times between trades or "duration", which in turn allows the modelling of price staleness effects. Option pricing models based on subdiffusions are incomplete, as they naturally account for the presence of a market risk of trade duration. However, when it comes to pricing this risk matters are quite subtle, since the subdiffusive Levy structure is not maintained under equivalent martingale measure changes unless the price of this risk is set to zero. We argue that this shortcoming can be resolved by introducing the broader class of tempered subdiffusive models. We highlight some additional features of tempered models that are consistent with economic stylized facts, and in particular explain the role of the stability and tempering parameters in capturing the time multiscaling properties of equity prices. Finally, we show that option pricing can be performed using standard integral representations.

Keywords: Duration risk, subdiffusions, tempered subdiffusions, derivative pricing, inverse tempered stable subordinator, Levy processes

JEL Classification: C65, G13

Suggested Citation

Torricelli, Lorenzo, Trade Duration Risk in Subdiffusive Financial Models (February 18, 2019). Available at SSRN: or

Lorenzo Torricelli (Contact Author)

University of Bologna Department of Statistics ( email )

Via Belle Arti
Bologna, 40121

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