Interest Rate Derivatives

Deep Hedging Bermudan Swaptions ArXiv ID: 2411.10079 “View on arXiv” Authors: Unknown Abstract Abstract This paper proposes a novel approach to Bermudan swaption hedging by applying the deep hedging framework to address limitations of traditional arbitrage-free methods. Conventional methods assume ideal conditions, such as zero transaction costs, perfect liquidity, and continuous-time hedging, which often differ from real market environments. This discrepancy can lead to residual profit and loss (P&L), resulting in two primary issues. First, residual P&L may prevent achieving the initial model price, especially with improper parameter settings, potentially causing a negative P&L trend and significant financial impacts. Second, controlling the distribution of residual P&L to mitigate downside risk is challenging, as hedged positions may become curve gamma-short, making them vulnerable to large interest rate movements. The deep hedging approach enables flexible selection of convex risk measures and hedge strategies, allowing for improved residual P&L management. This study also addresses challenges in applying the deep hedging approach to Bermudan swaptions, such as efficient arbitrage-free market scenario generation and managing early exercise conditions. Additionally, we introduce a unique “Option Spread Hedge” strategy, which allows for robust hedging and provides intuitive interpretability. Numerical analysis results demonstrate the effectiveness of our approach. ...

A case study on different one-factor Cheyette models for short maturity caplet calibration ArXiv ID: 2408.11257 “View on arXiv” Authors: Unknown Abstract In [“1”], we calibrated a one-factor Cheyette SLV model with a local volatility that is linear in the benchmark forward rate and an uncorrelated CIR stochastic variance to 3M caplets of various maturities. While caplet smiles for many maturities could be reasonably well calibrated across the range of strikes, for instance the 1Y maturity could not be calibrated well across that entire range of strikes. Here, we study whether models with alternative local volatility terms and/or alternative stochastic volatility or variance models can calibrate the 1Y caplet smile better across the strike range better than the model studied in [“1”]. This is made possible and feasible by the generic simulation, pricing, and calibration frameworks introduced in [“1”] and some new frameworks presented in this paper. We find that some model settings calibrate well to the 1Y smile across the strike range under study. In particular, a model setting with a local volatility that is piece-wise linear in the benchmark forward rate together with an uncorrelated CIR stochastic variance and one with a local volatility that is linear in the benchmark rate together with a correlated lognormal stochastic volatility with quadratic drift (QDLNSV) as in [“2”] calibrate well. We discuss why the later might be a preferable model. [“1”] Arun Kumar Polala and Bernhard Hientzsch. Parametric differential machine learning for pricing and calibration. arXiv preprint arXiv:2302.06682 , 2023. [“2”] Artur Sepp and Parviz Rakhmonov. A Robust Stochastic Volatility Model for Interest Rate Dynamics. Risk Magazine, 2023 ...

On the Hull-White model with volatility smile for Valuation Adjustments ArXiv ID: 2403.14841 “View on arXiv” Authors: Unknown Abstract Affine Diffusion dynamics are frequently used for Valuation Adjustments (xVA) calculations due to their analytic tractability. However, these models cannot capture the market-implied skew and smile, which are relevant when computing xVA metrics. Hence, additional degrees of freedom are required to capture these market features. In this paper, we address this through an SDE with state-dependent coefficients. The SDE is consistent with the convex combination of a finite number of different AD dynamics. We combine Hull-White one-factor models where one model parameter is varied. We use the Randomized AD (RAnD) technique to parameterize the combination of dynamics. We refer to our SDE with state-dependent coefficients and the RAnD parametrization of the original models as the rHW model. The rHW model allows for efficient semi-analytic calibration to European swaptions through the analytic tractability of the Hull-White dynamics. We use a regression-based Monte-Carlo simulation to calculate exposures. In this setting, we demonstrate the significant effect of skew and smile on exposures and xVAs of linear and early-exercise interest rate derivatives. ...

Cross-Currency Heath-Jarrow-Morton Framework in the Multiple-Curve Setting ArXiv ID: 2312.13057 “View on arXiv” Authors: Unknown Abstract We provide a general HJM framework for forward contracts written on abstract market indices with arbitrary fixing and payment adjustments, and featuring collateralization in any currency denominations. In view of this, we first provide a thorough study of cross-currency markets in the presence of collateral and incompleteness. Then we give a general treatment of collateral dislocations by describing the instantaneous cross-currency basis spreads by means of HJM models, for which we derive appropriate drift conditions. The framework obtained allows us to simultaneously cover forward-looking risky IBOR rates, such as EURIBOR, and backward-looking rates based on overnight rates, such as SOFR. Due to the discrepancies in market conventions of different currency areas created by the benchmark transition, this is pivotal for describing portfolios of interest-rate products that are denominated in multiple currencies. As an example of contract simultaneously depending on all the risk factors that we describe within our framework, we treat cross-currency swaps using our proposed abstract indices. ...