The Recalibration Conundrum: Hedging Valuation Adjustment for Callable Claims

TL;DR

This paper explores the challenge of recalibration in dynamic hedging of callable claims, proposing a model risk adjustment that accounts for exercise decision errors, which can significantly exceed traditional valuation-based reserves.

Contribution

It extends the hedging valuation adjustment (HVA) framework to callable assets, incorporating model risk and exercise decision errors into hedging strategies.

Findings

Model risk reserves can be much larger when accounting for exercise errors.

Recalibration impacts hedging strategies and valuation adjustments.

The approach is demonstrated on a stylized callable range accrual.

Abstract

The dynamic hedging theory only makes sense in the setup of one given model, whereas the practice of dynamic hedging is just the opposite, with models fleeing after the data through daily recalibration. This is quite of a quantitative finance paradox. In this paper we revisit Burnett (2021) \& Burnett and Williams (2021)'s notion of hedging valuation adjustment (HVA), originally intended to deal with dynamic hedging frictions, in the direction of recalibration and model risks. Specifically, we extend to callable assets the HVA model risk approach of B{\'e}n{\'e}zet and Cr{\'e}pey (2024). The classical way to deal with model risk is to reserve the differences between the valuations in reference models and in the local models used by traders. However, while traders' prices are thus corrected, their hedging strategies and their exercise decisions are still wrong, which necessitates a risk-adjusted reserve. We illustrate our approach on a stylized callable range accrual representative of huge amounts of structured products on the market. We show that a model risk reserve adjusted for the risk of wrong exercise decisions may largely exceed a basic reserve only accounting for valuation differences.