Hedging error as generalized timing risk

Abstract

This paper introduces a methodology to disentangle the hedging error associated with the hedging of exotic derivatives, whose payment time is unknown at inception. We derive the mathematical representation for a one-dimensional setting: we identify and characterize the hedging error and discuss the economic intuition of hedging error as a generalized timing risk. We then provide its mathematical integral representation to: (i) disentangle the hedging error into a specific set of positions in barrier options, (ii) re-iterate the procedure to the second order to reduce the hedging error cost. We provide an illustrative example via a dedicated numerical study. From a theoretical point of view, this paper states the foundations for future extensions in the directions of: (i) building a general multidimensional framework, (ii) re-iterating the procedure to higher orders, (iii) investigate the bridge with advanced analytics methodologies and techniques.