Hedging error as generalized timing risk

Akahori, J.; Barsotti, F.B.; Imamura, Y.

doi:10.1080/14697688.2022.2154255

Hedging error as generalized timing risk

Title

Hedging error as generalized timing risk

Author

Akahori, J. (Ritsumeikan University, Biwako-Kusatsu)
Barsotti, F.B. (TU Delft Applied Probability; Universiteit van Amsterdam)
Imamura, Y. (Kanazawa University)

Date

2023

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.

Subject

Barrier options
Hedging error
Semi-static hedge
Timing risk

To reference this document use:

http://resolver.tudelft.nl/uuid:b71371e5-cf27-4590-85d6-da7727083426

DOI

https://doi.org/10.1080/14697688.2022.2154255

ISSN

1469-7688

Source

Quantitative Finance, 23 (4), 693-703

Part of collection

Institutional Repository