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The Recalibration Conundrum: Hedging Valuation Adjustment for Callable Claims

Cyril Bénézet, Stéphane Crépey, Dounia Essaket

TL;DR

This paper tackles recalibration risk in hedging callable claims by extending the Hedging Valuation Adjustment (HVA) framework to a dual-model setting with callable assets, enabling a risk-adjusted reserve beyond mere valuation differences. It defines HVA as a decomposition of misvaluation and hedging/exercise risks, and couples it with a KVA that funds economic capital at a target hurdle rate, within a discrete-time, stylized callable range accrual. The study contrasts a Bad Trader and a Not-So-Bad Trader to quantify how recalibration-driven mispricing and suboptimal exercise propagate through HVAs and KVAs, demonstrating that HVA can dominate simple valuation gaps. Numerical results show explicit, tractable calculations via exact dynamic programming in the discrete setup, illuminating the magnitude and structure of recalibration risk and its impact on capital reserves. The findings underscore the importance of accounting for hedging and exercise misspecification in model-risk reserves and suggest that practitioners consider strong model governance to mitigate large HVA/KVA costs in callable structured products.

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.

The Recalibration Conundrum: Hedging Valuation Adjustment for Callable Claims

TL;DR

This paper tackles recalibration risk in hedging callable claims by extending the Hedging Valuation Adjustment (HVA) framework to a dual-model setting with callable assets, enabling a risk-adjusted reserve beyond mere valuation differences. It defines HVA as a decomposition of misvaluation and hedging/exercise risks, and couples it with a KVA that funds economic capital at a target hurdle rate, within a discrete-time, stylized callable range accrual. The study contrasts a Bad Trader and a Not-So-Bad Trader to quantify how recalibration-driven mispricing and suboptimal exercise propagate through HVAs and KVAs, demonstrating that HVA can dominate simple valuation gaps. Numerical results show explicit, tractable calculations via exact dynamic programming in the discrete setup, illuminating the magnitude and structure of recalibration risk and its impact on capital reserves. The findings underscore the importance of accounting for hedging and exercise misspecification in model-risk reserves and suggest that practitioners consider strong model governance to mitigate large HVA/KVA costs in callable structured products.

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.
Paper Structure (26 sections, 13 theorems, 80 equations, 10 figures, 3 tables)

This paper contains 26 sections, 13 theorems, 80 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Setup
  3. Outline and Notation
  4. HVA for Callables: Abstract Framework
  5. Hedging Valuation Adjustment
  6. Capital Valuation Adjustment
  7. The Bad and Not-So-Bad Traders
  8. Stylized Callable Range Accrual in Discrete Time
  9. Pricing and Hedging
  10. Hedging assets and calibration of the local model
  11. Range accrual and its hedging ratios
  12. Bad Trader's XVAs
  13. Not-So-Bad Trader's XVAs
  14. Numerical Results
  15. Bad Trader
  16. ...and 11 more sections

Key Result

Proposition 2.1

Under Assumption hyp:recalib, we have, for all $t \in \mathbb T$,

Figures (10)

  • Figure 1: Jump intensities, pricing, and greeking functions.
  • Figure 2: (center) bad trader's $pnl\xspace$, (top) callable option cash flow and price minus its hedge cash flow and price, (bottom) term accounting for calling the product (at zero recovery).
  • Figure 3: Bad trader's ${\rm HVA}$ and its components.
  • Figure 4: HVA-compensated loss-and-profits of the bad trader.
  • Figure 5: Not-so-bad trader's ${\rm HVA}$ and its components.
  • ...and 5 more figures

Theorems & Definitions (29)

  • Remark 1.1
  • Remark 1.2
  • Definition 2.1
  • Remark 2.1
  • Definition 2.3
  • Proposition 2.1
  • Remark 2.2
  • Definition 2.4
  • Remark 2.3
  • Definition 2.5
  • ...and 19 more