Paper: arXiv 2304.02479

Authors: Cyril Bénézet, Stéphane Crépey, Dounia Essaket

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{é}n{é}zet and Cr{é}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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a mathematically sophisticated extension of Hedging Valuation Adjustment (HVA) to callable claims, addressing the real-world paradox of model recalibration risk. While the theoretical framework and application to range accruals are strong and novel, empirical validation is limited to stylized numerical illustrations rather than extensive market backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal: Quantify Model Risk & Exercise Error Reserve (HVA) for Callable Claims"] --> B["Inputs: Stylized Callable Range Accrual & Rates Data"]
    B --> C["Extend Bénézet & Crépey (2024) Framework to Callable Assets"]
    C --> D["Simulate Local Model vs Reference Model (Daily Recalibration)"]
    D --> E["Compute HVA: Valuation Differences + Risk-Adjusted Wrong Exercise Strategy"]
    E --> F["Key Outcome: Reserve accounting for wrong exercise risk largely exceeds basic valuation reserve"]