Hedging Valuation Adjustment for Callable Claims

In this work, we extend to callable assets the model risk approach of B{\'e}n{\'e}zet and Cr{\'e}pey (2024), itself leveraging on the notion of hedging valuation adjustment initially introduced for dealing with transaction costs in Burnett (2021) \& Burnett and Williams (2021). 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 showthat a model risk reserve adjusted for the risk of wrong exercise decisions may largely exceed a basic reserve only accounting for valuation differences.