Interest Rate Derivatives And Value At Risk With Multiscale Stochastic Volatility
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Author | : Rafael de Santiago |
Publisher | : |
Total Pages | : 418 |
Release | : 2007 |
Genre | : Derivative securities |
ISBN | : 9781109910087 |
Download Interest Rate Derivatives and Value at Risk with Multiscale Stochastic Volatility Book in PDF, Epub and Kindle
We apply perturbation methods as well to Value-at-Risk (VaR), a measure of portfolio risk. Once a confidence level q is fixed, we first compute an approximation to the distribution function of the value of the portfolio, and using this approximation we then obtain an asymptotic approximation to the q-quantile of the distribution.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 2005 |
Genre | : |
ISBN | : 9781139155267 |
Download Volatility Perturbations in Financial Markets Book in PDF, Epub and Kindle
Author | : Jean-Pierre Fouque |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 2011-09-29 |
Genre | : Mathematics |
ISBN | : 113950245X |
Download Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives Book in PDF, Epub and Kindle
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
Author | : Jörg Kienitz |
Publisher | : Springer |
Total Pages | : 261 |
Release | : 2017-11-08 |
Genre | : Business & Economics |
ISBN | : 1137360194 |
Download Interest Rate Derivatives Explained: Volume 2 Book in PDF, Epub and Kindle
This book on Interest Rate Derivatives has three parts. The first part is on financial products and extends the range of products considered in Interest Rate Derivatives Explained I. In particular we consider callable products such as Bermudan swaptions or exotic derivatives. The second part is on volatility modelling. The Heston and the SABR model are reviewed and analyzed in detail. Both models are widely applied in practice. Such models are necessary to account for the volatility skew/smile and form the fundament for pricing and risk management of complex interest rate structures such as Constant Maturity Swap options. Term structure models are introduced in the third part. We consider three main classes namely short rate models, instantaneous forward rate models and market models. For each class we review one representative which is heavily used in practice. We have chosen the Hull-White, the Cheyette and the Libor Market model. For all the models we consider the extensions by a stochastic basis and stochastic volatility component. Finally, we round up the exposition by giving an overview of the numerical methods that are relevant for successfully implementing the models considered in the book.
Author | : Antoine Petrus Cornelius van der Ploeg |
Publisher | : Rozenberg Publishers |
Total Pages | : 358 |
Release | : 2006 |
Genre | : |
ISBN | : 9051705778 |
Download Stochastic volatility and the pricing of financial derivatives Book in PDF, Epub and Kindle
Author | : Lin Chen |
Publisher | : |
Total Pages | : 88 |
Release | : 1996 |
Genre | : Interest rates |
ISBN | : |
Download Stochastic Mean and Stochastic Volatility Book in PDF, Epub and Kindle
Author | : Anders B. Trolle |
Publisher | : |
Total Pages | : 62 |
Release | : 2006 |
Genre | : Interest rates |
ISBN | : |
Download A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives Book in PDF, Epub and Kindle
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 | : Anders B. Trolle |
Publisher | : |
Total Pages | : 66 |
Release | : 2016 |
Genre | : |
ISBN | : |
Download A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives Book in PDF, Epub and Kindle
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 | : Tianyu Liang |
Publisher | : |
Total Pages | : |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : |
Download Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives Book in PDF, Epub and Kindle
ABSTRACT: A lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the mean-reverting process from a constant to a function of the underlying process. We apply our models to the pricing of both equity and interest rate derivatives. Throughout the thesis, a singular perturbation method is employed to derive closed-form formulas up to first order asymptotic solutions. We also implement multiplicative noise to arithmetic Ornstein-Uhlenbeck process to produce a wider variety of effects. Calibration and Monte Carlo simulation results show that the proposed model outperform Fouque's original stochastic volatility model during some particular window in history. A more efficient numerical scheme, the heterogeneous multi-scale method (HMM), is introduced to simulate the multi-scale differential equations discussed over the chapters.
Author | : Linus Kaisajuntti |
Publisher | : |
Total Pages | : 46 |
Release | : 2019 |
Genre | : |
ISBN | : |
Download Stochastic Volatility for Interest Rate Derivatives Book in PDF, Epub and Kindle
This paper uses an extensive set of market data of forward swap rates and swaptions covering 3 July 2002 to 21 May 2009 to identify a two-dimensional stochastic volatility process for the level of rates. The process is identified step by step by increasing the requirement of the model and introduce appropriate adjustments.The first part of the paper investigates the smile dynamics of forward swap rates at their setting dates. Comparing the SABR (with different $ beta$s) and Heston stochastic volatility models informs about what different specifications of the driving SDEs has to offer in terms of reflecting the dynamics of the smile across dates. The outcome of the analysis is that a normal SABR model ($ beta=0$) satisfactorily passes all tests and seems to provide a good match to the market. In contrast we find the Heston model does not.The next step is to seek a model of the forward swap rates (in their own swaption measure) based on only two factors that enables a specification with common parameters. It turns out that this can be done by extending the SABR model with a time-dependent volatility function and a mean reverting volatility process. The performance of the extended (SABR with mean-reversion) model is analysed over several historical dates and is shown to be a stable and flexible choice that allows for good calibration across expiries and strikes. Finally a time-homogeneous candidate stochastic volatility process that can be used as a driver for all swap rates is identified and used to construct a simple terminal Markov-functional type model under a single measure. This candidate process may in future work be used as a building block for a separable stochastic volatility LIBOR market model or a stochastic volatility Markov-functional model.