Calibration Methods of Hull-White Model

Gurrieri, Sébastien; Nakabayashi, Masaki; Wong, Tony Siu Tung

doi:10.2139/ssrn.1514192

Cited by 12 publications

(9 citation statements)

References 9 publications

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“…Also, notice that all calibrated parameters are somewhat volatile, especially for the two-factor HW model (where parameters are often close to the constraints). This phenomenon has been observed elsewhere in the literature (for example, Enev (2011) and Gurrieri et al (2009)). In Section 6, we will apply the hedging strategies derived from these models and parameters to realworld interest rate paths; we will demonstrate that in spite of the volatility in the implied parameters, the hedging strategies can nevertheless be quite effective.…”

Section: Estimating the Parameterssupporting

confidence: 81%

“…However, this one-factor model is not equivalent to the one-factor HW whenever a 1 = a 2 (see Brigo and Mercurio (2001)). Gurrieri et al (2009), Gupta and Subrahmanyam (2005) and Brigo and Mercurio (2001) all note that ρ may become highly negative depending on the instruments used for calibration. The parameter values shown above imply a long-term unconditional standard deviation for the short rate that is close to experience over the past 30-40 years.…”

Section: Estimating the Parametersmentioning

confidence: 99%

“…The most common choices of market derivatives used for calibration of interest rate models are caps and swaptions. We use swaptions as they contain more information on the correlations between forward rates, which is critical in our application (see Brigo and Mercurio (2001) example, Gurrieri et al (2009) compare the calibration results using three sets of swaptions for the one-factor HW with time-varying mean reversion and volatility. We use at-the-money swaptions with expiration dates between one year and the maturity of the CB liability.…”

Section: Estimating the Parametersmentioning

confidence: 99%

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Dynamic Hedging Strategies for Cash Balance Pension Plans

2018

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Cash balance pension plans with crediting rates linked to long bond yields are relatively common in the United States, but their liabilities are proving very challenging to hedge. In this paper, we consider dynamic hedge strategies using the one-factor and two-factor Hull White models, based on results for the liability valuation from Hardy et al. (2014). The strategies utilise simple hedge portfolios combining one or two zero-coupon bonds, and a money market account. We assess the effectiveness of the strategies by considering how accurately each one would have hedged a 5-year cash balance liability through the past 20 years, using real-world returns and crediting rates, and assuming parameters calibrated using the information available at the time. We show that there is considerable impact of model and parameter uncertainty, with additional, less severe impact from discrete hedging error and transactions costs. Despite this, the dynamic hedge strategies do manage to stabilize surplus substantially, even through the turbulence of the past two decades.

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Section: Estimating the Parameterssupporting

confidence: 81%

Section: Estimating the Parametersmentioning

confidence: 99%

Section: Estimating the Parametersmentioning

confidence: 99%

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Dynamic Hedging Strategies for Cash Balance Pension Plans

2018

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“…Remark 2.4: It is well known that affine short-rate models with positive mean-reversion speed cannot produce a humped implied volatility term structure as observed in the market. Gurrieri et al (2010) show, for the Hull-White model, that the humped implied volatility curve can be generated if the mean-reversion speed is allowed to be negative at the short end. Formulas (2.8)-(2.11) show that the OUB parameters are even functions of the mean-reversion speed κ, indicating that they are valid for negative mean-reversion speed.…”

Section: Remark 22mentioning

confidence: 96%

Modeling the Path-Dependency of the Credit Exposure in Vanilla Products

Zhou¹

2016

Wilmott

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This paper focuses on modeling the scenario path-dependency of the counterparty credit exposure. The purpose of this paper is threefold: (1) to propose a simple method for consistent estimation of pathwise European swaption exercise probability;(2) to discuss accurate pathwise simulation of barrier option exposure; and (3) to present some exact formulas for the calculation of standalone expected positive exposure and potential future exposure for a single-currency vanilla swap, a physically settled European swaption, and a barrier option without Monte Carlo simulation. These exact formulations are of practical importance to computing standalone exposure profiles, exposure model validation, and system benchmarking. Keywordspath-dependent exposure, exact exposure profile, swaption exercise probability, barrier survival probability 57 regardless of the number of coupons remaining, follow a single lognormal process. Schmöger (2012) published a detailed calculation based on the approach of Lomibao and Zhu (2006) for both a swaption and a barrier option. Schmöger calculated the swaption exposure only prior to the expiry date because, as he pointed out, "the forward swap rate does not exist after the swaption expiry" (Schmöger, 2012). This means that the forward swap rate for a swap starting at the option expiry ceases to exist past the expiry date, suggesting that the co-terminal swap rates cannot follow a single process.With the DJS, scenarios are generated independently, whereas with the pathwise approach, an entire path is simulated. While the two approaches theoretically generate the same distribution, Ghamami and Zhang (2014) showed that the pathwise approach generates a drastically smaller MSE (mean-squared error) than the DJS. Gregory (2012) also pointed out that a pathwise simulation approach is preferred. In this paper, we demonstrate that the DJS barrier survival probability does not decrease with time.An issue with using a single lognormal swap rate model for swaption exposure in the conditional approach is that a single swap rate model is inconsistent with all the swap rates of the co-terminal swaps spanning the underlying swap, as the number of swap payments decreases with the passage of time. It is clear from the swap rate definition, equation (3.6), that the swap rate depends specifically on the swap term. We show why this is the case and present an alternative approach. This paper has three goals. First, it presents a model for the pathwise probability that a European swaption will be exercised and that the exposure will persist beyond the option expiration date. Our model is based on an Ornstein-Uhlenbeck bridge (OUB) (Corlay, 2014), where the pathwise swaption exercise probability is consistent with the pathwise swap valuation both before and after the option expiry date. Second, it discusses a pathwise approach to the barrier hitting probability. This model takes into account information on the full Monte Carlo path. It demonstrates that the pathwise barrier hitting probability can be significantly d...

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“…For example, in the first part of the series we showed that the HW 1F model is capable of simultaneously producing meaningful xVAs for a number of interest rate swaps that differ by maturity, provided that suitable swaptions -swaptions arranged in a chevron pattern that partially track the swaps' exposure peaks -are used for the volatility calibration. The calculations, without having gone into detail there, however, also took advantage of a fine-tuning procedure aimed at the mean reversion parameter [4,5]. The mean reversion parameter is a crucial additional model degree of freedom that can significantly affect exposure simulations and xVA estimates.…”

mentioning

confidence: 99%

One‐Factor Hull—White Model Calibration for CVA Part II: Optimizing the Mean Reversion Parameter

Puetter¹,

Renzitti²

2020

Wilmott

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This paper is the second of a multi‐part series on the calibration of the one‐factor Hull—White short rate model for the purpose of computing CVAs (and XVas) with an XVa system. The first part introduces an atypical bootstrapping scheme for the calibration of the short rate volatility. The present second part focuses on the selection of the mean reversion parameter. In both expositions we present long‐term time series results for EUR, JPY, and USD, covering the period from the beginning of 2009 (at the earliest) to spring 2020.

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Calibration Methods of Hull-White Model

Cited by 12 publications

References 9 publications

Dynamic Hedging Strategies for Cash Balance Pension Plans

Dynamic Hedging Strategies for Cash Balance Pension Plans

Modeling the Path-Dependency of the Credit Exposure in Vanilla Products

One‐Factor Hull—White Model Calibration for CVA Part II: Optimizing the Mean Reversion Parameter

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