The nature of the dependence of the magnitude of rate moves on the rates levels: a universal relationship

Deguillaume, Nick; Rebonato, Riccardo; Pogudin, Andrey

doi:10.1080/14697688.2012.740569

Cited by 31 publications

(9 citation statements)

References 21 publications

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“…Finally, we calibrate the model to market data on interest rate caps between 2004 and 2013. Interestingly, we find that market prices are consistent with recent empirical research by DeGuillaume et al (2013). White (1994, 1996) consider models of the form…”

Section: Introductionsupporting

confidence: 86%

A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions

Hull

White

2014

Quantitative Finance

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One-factor no-arbitrage models of the short rate are important tools for valuing interest rate derivatives. Trees are often used to implement the models and fit them to the initial term structure. This paper generalizes existing tree building procedures so that a very wide range of interest rate models can be accommodated. It shows how a piecewise linear volatility function can be calibrated to market data and, using market data from days during the period 2004-2013, finds a best fit to cap prices.

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Section: Introductionsupporting

confidence: 86%

A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions

Hull

White

2014

Quantitative Finance

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“…The process followed by the instantaneous OIS rate was similar to that derived by Deguillaume, Rebonato and Pogodin [7], and Hull and White [16]. For short rates between 0 and 1.5 %, changes in the rate are assumed to be lognormal with a volatility of 100 %.…”

Section: Bermudan Swap Optionmentioning

confidence: 84%

“…Monte Carlo simulation is usually used in these situations. 7 This model does not allow interest rates to become negative. Negative interest have been observed in some currencies (particularly the euro and Swiss franc).…”

Section: The Methodologymentioning

confidence: 99%

“…The function θ(t) is chosen to match the initial term structure of OIS rates; a r (≥0) is the reversion rate of x; σ r (>0) is the volatility of r ; and dz r is a Wiener process. 7 Define s as the spread between the LIBOR rate with tenor τ and the OIS rate with tenor τ (both rates being measured with a compounding frequency corresponding to the tenor). We assume that some function of s, y(s), follows the process:…”

Section: The Methodologymentioning

confidence: 99%

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Multi-curve Modelling Using Trees

Hull

White

2016

Innovations in Derivatives Markets

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Since 2008 the valuation of derivatives has evolved so that OIS discounting rather than LIBOR discounting is used. Payoffs from interest rate derivatives usually depend on LIBOR. This means that the valuation of interest rate derivatives depends on the evolution of two different term structures. The spread between OIS and LIBOR rates is often assumed to be constant or deterministic. This paper explores how this assumption can be relaxed. It shows how well-established methods used to represent one-factor interest rate models in the form of a binomial or trinomial tree can be extended so that the OIS rate and a LIBOR rate are jointly modelled in a threedimensional tree. The procedures are illustrated with the valuation of spread options and Bermudan swap options. The tree is constructed so that LIBOR swap rates are matched.

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“…The results of these tests for the six most significant forward rate based principal components of the Blomvall (2017) dataset are found in Table 4. Deguillaume et al (2013) empirically show that the interest rate volatility is dependent on the interest rate levels in certain regimes. For low interest rates, below 2%, and for high interest rates, above 6%, interest rate volatility increases proportionally to the interest rate level.…”

Section: Volatility and Scenario Modelingmentioning

confidence: 99%

Simulation and evaluation of the distribution of interest rate risk

Hagenbjörk

Blomvall

2018

Comput Manag Sci

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We study methods to simulate term structures in order to measure interest rate risk more accurately. We use principal component analysis of term structure innovations to identify risk factors and we model their univariate distribution using GARCH-models with Student's t-distributions in order to handle heteroscedasticity and fat tails. We find that the Student's t-copula is most suitable to model codependence of these univariate risk factors. We aim to develop a model that provides low ex-ante risk measures, while having accurate representations of the ex-post realized risk. By utilizing a more accurate term structure estimation method, our proposed model is less sensitive to measurement noise compared to traditional models. We perform an out-of-sample test for the U.S. market between 2002 and 2017 by valuing a portfolio consisting of interest rate derivatives. We find that ex-ante Value at Risk measurements can be substantially reduced for all confidence levels above 95%, compared to the traditional models. We find that that the realized portfolio tail losses accurately conform to the ex-ante measurement for daily returns, while traditional methods overestimate, or in some cases even underestimate the risk ex-post. Due to noise inherent in the term structure measurements, we find that all models overestimate the risk for 10-day and quarterly returns, but that our proposed model provides the by far lowest Value at Risk measures.

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The nature of the dependence of the magnitude of rate moves on the rates levels: a universal relationship

Cited by 31 publications

References 21 publications

A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions

A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions

Multi-curve Modelling Using Trees

Simulation and evaluation of the distribution of interest rate risk

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