An Arbitrage-Free Nelson-Siegel Model with Unspanned Stochastic Volatility for the Pricing of Interest Rate Derivatives PDF Download
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Author: Rui Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
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Book Description
We propose a generalized arbitrage-free Nelson-Siegel model under the HJM framework. It features unspanned stochastic volatility factors while maintaining a Nelson-Siegel factor loading structure. The price of the interest rate derivatives, including European options, Caps and Swaptions are then obtained in semi closed-form. We calibrate the model using an extensive panel data, including the US Libor rates, Swap rates, caps and swaptions. By estimating our model via the extended Kalman filter, we find strong evidence that our model prices interest rates and their derivatives accurately.
Author: Rui Chen
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
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Book Description
We propose a generalized arbitrage-free Nelson-Siegel model under the HJM framework. It features unspanned stochastic volatility factors while maintaining a Nelson-Siegel factor loading structure. The price of the interest rate derivatives, including European options, Caps and Swaptions are then obtained in semi closed-form. We calibrate the model using an extensive panel data, including the US Libor rates, Swap rates, caps and swaptions. By estimating our model via the extended Kalman filter, we find strong evidence that our model prices interest rates and their derivatives accurately.
Author: Anders B. Trolle
Publisher:
ISBN:
Category :
Languages : en
Pages : 66
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Book Description
We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zero-coupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities.
Author:
Publisher: ScholarlyEditions
ISBN: 1490106804
Category : Business & Economics
Languages : en
Pages : 241
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Book Description
Issues in Finance, Business, and Economics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about Additional Research. The editors have built Issues in Finance, Business, and Economics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Additional Research in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Finance, Business, and Economics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Author: Zhiwu Hong
Publisher:
ISBN:
Category :
Languages : en
Pages : 45
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Book Description
We characterize the discrete-time arbitrage-free Nelson-Siegel term structure model, prove the uniqueness of the solution for model identification, make specification analysis on its canonical form, and detail the MCMC estimation method with a fast and reliable prior extraction step. Using the model, we examine how the yield curves of U.S. and China react to exchange rate policy shocks from China in its gradual reform to a more flexible exchange rate regime. Model decomposition reveals that, in U.S. yield responses, changes in risk premia for medium- to long-term yields dominate changes in yield expectation for short- to medium-term yields. The results are helpful to diagnosing market sentiment and exchange rate risk pricing as China further internationalizes its currency.
Author: Antoine Petrus Cornelius van der Ploeg
Publisher: Rozenberg Publishers
ISBN: 9051705778
Category :
Languages : en
Pages : 358
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Book Description
Author: Claus Munk
Publisher: Oxford University Press
ISBN: 0199575088
Category : Business & Economics
Languages : en
Pages : 573
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Book Description
A large number of securities related to various interest rates are traded in financial markets. Traders and analysts in the financial industry apply models based on economics, mathematics and probability theory to compute reasonable prices and risk measures for these securities. This book offers a unified presentation of such models and securities.
Author: Jens H. E. Christensen
Publisher:
ISBN:
Category : Econometric models
Languages : en
Pages : 54
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Book Description
We derive the class of arbitrage-free affine dynamic term structure models that approximate the widely-used Nelson-Siegel yield-curve specification. Our theoretical analysis relates this new class of models to the canonical representation of the three-factor arbitrage-free affine model. Our empirical analysis shows that imposing the Nelson-Siegel structure on this canonical representation greatly improves its empirical tractability; furthermore, we find that improvements in predictive performance are achieved from the imposition of absence of arbitrage.
Author: Anders B. Trolle
Publisher:
ISBN:
Category :
Languages : en
Pages : 64
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Book Description
We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasi-analytical prices of zero-coupon bond options and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.
Author: Lin Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In this paper a three-factor model of the term structure of interest rates is developed. In the model the future short rate depends on 1) the current short rate, 2) the short-term mean of the short rate, and 3) the current volatility of the short rate. Furthermore, it is assumed that both the short term mean of the short rate and the volatility of the short rate are stochastic and follow square-root process. The model is a substantial extension the seminal Cox-Ingersoll-Ross model of interest rates. A general formula for evaluating interest rate derivatives is presented. Closed-form solutions for prices of bond, bond option, futures, futures option, swap and cap are derived. The model can fit into the Heath-Jarrow-Morton arbitrage framework. The model is also useful for other practical purposes such as managing interest rate risks and formulating fixed income arbitrage strategies.
Author: Dariusz Gatarek
Publisher:
ISBN:
Category :
Languages : en
Pages : 8
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Book Description
Four papers introducing LIBOR market model (LMM) were published in 1997. They seemed to unify market practice with arbitrage-free framework - it came out that for one year only. The next year, after Russian crisis, cap and swaption markets started to show evident volatility smile and skew. Several attempts were made to capture that phenomenon into the arbitrage-free framework. Our note is strongly inspired by papers and conference talks by Mark Joshi and Riccardo Rebonato. We share their opinions that:- Since smiles and skews are caused by different market features, it is more natural to model smile and skew separately, rather then to use unified framework of implied smile.- Displaced Diffusion approach is easier in treatment then Constant Elasticity of Variance (CEV) approach for interest rate derivatives and gives the same modelling possibilities.- Displaced Diffusion and Stochastic Volatility are perfectly suited to work together.Since our attention is fixed more on swaptions then on caps/floors, we would like to opt for another version of the LIBOR market model with stochastic volatility and displaced diffusion (SVDDLMM) then Joshi and Rebonato:- We use various random displacement factors for various LIBOR rates. - For Stochastic Volatility we propose a new simple non mean reverting multi-lognormal model. We also try to convince the Reader that mean reversion in stochastic volatility models excludes correct modelling of long term options - swaptions are canonical example.Easy closed form formulae are given for caps/floors and European swaptions what makes calibration procedure more effective and transparent - at least we are not quot;prisoners of Monte Carloquot;. We are able to calibrate model to various smile/skew shapes for caps/floors and swaptions with various length and of various maturities.
