Stochastic Volatility Extensions Of The Swap Market Model

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Stochastic Volatility Extensions of the Swap Market Model

Author : Milena Gueorguieva Tzigantcheva
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (39 download)

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Book Synopsis Stochastic Volatility Extensions of the Swap Market Model by : Milena Gueorguieva Tzigantcheva

Download or read book Stochastic Volatility Extensions of the Swap Market Model written by Milena Gueorguieva Tzigantcheva and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Two stochastic volatility extensions of the Swap Market Model, one with jumps and the other without, are derived. In both stochastic volatility extensions of the Swap Market Model the instantaneous volatility of the forward swap rates evolves according to a square-root diffusion process. In the jump-diffusion stochastic volatility extension of the Swap Market Model, the proportional log-normal jumps are applied to the swap rate dynamics. The speed, the flexibility and the accuracy of the fast fractional Fourier transform made possible a fast calibration to European swaption market prices. A specific functional form of the instantaneous swap rate volatility structure was used to meet the observed evidence that volatility of the instantaneous swap rate decreases with longer swaption maturity and with larger swaption tenors.

Multicurrency Extension of a Multiple Stochastic Volatility Libor Market Model

Author : Stanley Mathew
Publisher :
ISBN 13 :
Total Pages : 193 pages
Book Rating : 4.:/5 (423 download)

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Book Synopsis Multicurrency Extension of a Multiple Stochastic Volatility Libor Market Model by : Stanley Mathew

Download or read book Multicurrency Extension of a Multiple Stochastic Volatility Libor Market Model written by Stanley Mathew and published by . This book was released on 2009 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Swap Market Model with Local Stochastic Volatility

Author : Kenjiro Oya
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis The Swap Market Model with Local Stochastic Volatility by : Kenjiro Oya

Download or read book The Swap Market Model with Local Stochastic Volatility written by Kenjiro Oya and published by . This book was released on 2018 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to present the multi-factor swap market model with non-parametric local volatility functions and stochastic volatility scaling factors. We provide a Dupire-like formula with which calibration can be carried out with the particle algorithm in an efficient manner. We also discuss how the calibration method can be made applicable in the context of Libor Market Model. We show high accuracy of our calibration algorithm by numerical experiments.

Study and Calibration of a LIBOR Forward Swap Model with Stochastic Volatility

Author : Giorgio Mori
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Study and Calibration of a LIBOR Forward Swap Model with Stochastic Volatility by : Giorgio Mori

Download or read book Study and Calibration of a LIBOR Forward Swap Model with Stochastic Volatility written by Giorgio Mori and published by . This book was released on 2013 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this master thesis is the study of a LIBOR forward swap model with stochastic volatility and its calibration based on the market European swaption implied volatility surface. The first part of the thesis will briefly review the most common short rate models; it will introduce the Heath-Jarrow-Morton framework and it will describe the LIBOR swap Market Model (LMM). The topic of the second part will be the extension of the LMM including a stochastic term in the forward rate volatility. In particular the thesis will follow the approach described by Wu and Zhang 2006. This approach allows a calibration of the LMM parameters to an European swaption implied volatility surface making it particularly interesting for applications in the financial industry. In the third part, the numerical implementation of the model will be described and the calibration procedures and results will be discussed. The conclusions will summarize the key features of the stochastic volatility LMM and will discuss the main results.

The Co-Terminal Swap Market Model with Bergomi Stochastic Volatility

Author : Kenjiro Oya
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis The Co-Terminal Swap Market Model with Bergomi Stochastic Volatility by : Kenjiro Oya

Download or read book The Co-Terminal Swap Market Model with Bergomi Stochastic Volatility written by Kenjiro Oya and published by . This book was released on 2018 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we apply the forward variance modeling approach by L.Bergomi to the co-terminal swap market model. We build an interest rate model for which all the market price changes of hedging instruments, interest rate swaps and European swaptions, are interpreted as the state variable variations, and no diffusion parameter calibration procedure is required. The model provides quite simple profit and loss (PnL) formula, with which we can easily understand where a material PnL trend comes from when it appears, and consider how we should modify the model parameters. The model has high flexibility to control the model dynamics because parameter calibration is unnecessary and the model parameters can be used solely for the purpose of the model dynamics control. With the model, the position management of the exotic interest rate products, e.g. Bermudan swaptions, can be carried out in a more sophisticated and systematic manner. A numerical experiment is performed to show the effectiveness of the approach for a Canary swaption, which is a special form of a Bermudan swaption.

Interest Rate Derivatives Explained: Volume 2

Author : Jörg Kienitz
Publisher : Springer
ISBN 13 : 1137360194
Total Pages : 261 pages
Book Rating : 4.1/5 (373 download)

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Book Synopsis Interest Rate Derivatives Explained: Volume 2 by : Jörg Kienitz

Download or read book Interest Rate Derivatives Explained: Volume 2 written by Jörg Kienitz and published by Springer. This book was released on 2017-11-08 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The SABR/LIBOR Market Model

Author : Riccardo Rebonato
Publisher : John Wiley & Sons
ISBN 13 : 1119995639
Total Pages : 308 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis The SABR/LIBOR Market Model by : Riccardo Rebonato

Download or read book The SABR/LIBOR Market Model written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2011-03-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a major innovation in the interest rate space. It explains a financially motivated extension of the LIBOR Market model which accurately reproduces the prices for plain vanilla hedging instruments (swaptions and caplets) of all strikes and maturities produced by the SABR model. The authors show how to accurately recover the whole of the SABR smile surface using their extension of the LIBOR market model. This is not just a new model, this is a new way of option pricing that takes into account the need to calibrate as accurately as possible to the plain vanilla reference hedging instruments and the need to obtain prices and hedges in reasonable time whilst reproducing a realistic future evolution of the smile surface. It removes the hard choice between accuracy and time because the framework that the authors provide reproduces today's market prices of plain vanilla options almost exactly and simultaneously gives a reasonable future evolution for the smile surface. The authors take the SABR model as the starting point for their extension of the LMM because it is a good model for European options. The problem, however with SABR is that it treats each European option in isolation and the processes for the various underlyings (forward and swap rates) do not talk to each other so it isn't obvious how to relate these processes into the dynamics of the whole yield curve. With this new model, the authors bring the dynamics of the various forward rates and stochastic volatilities under a single umbrella. To ensure the absence of arbitrage they derive drift adjustments to be applied to both the forward rates and their volatilities. When this is completed, complex derivatives that depend on the joint realisation of all relevant forward rates can now be priced. Contents THE THEORETICAL SET-UP The Libor Market model The SABR Model The LMM-SABR Model IMPLEMENTATION AND CALIBRATION Calibrating the LMM-SABR model to Market Caplet prices Calibrating the LMM/SABR model to Market Swaption Prices Calibrating the Correlation Structure EMPIRICAL EVIDENCE The Empirical problem Estimating the volatility of the forward rates Estimating the correlation structure Estimating the volatility of the volatility HEDGING Hedging the Volatility Structure Hedging the Correlation Structure Hedging in conditions of market stress

Stochastic Volatility for Interest Rate Derivatives

Author : Linus Kaisajuntti
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Stochastic Volatility for Interest Rate Derivatives by : Linus Kaisajuntti

Download or read book Stochastic Volatility for Interest Rate Derivatives written by Linus Kaisajuntti and published by . This book was released on 2019 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Volatility Modeling

Author : Lorenzo Bergomi
Publisher : CRC Press
ISBN 13 : 1482244071
Total Pages : 520 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Stochastic Volatility Modeling by : Lorenzo Bergomi

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c

Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities

Author : Anatoli? Vital?evich Svishchuk
Publisher : World Scientific
ISBN 13 : 9814440132
Total Pages : 326 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities by : Anatoli? Vital?evich Svishchuk

Download or read book Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities written by Anatoli? Vital?evich Svishchuk and published by World Scientific. This book was released on 2013 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.

Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process

Author : Lech A. Grzelak
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process by : Lech A. Grzelak

Download or read book Extension of Stochastic Volatility Equity Models with Hull-White Interest Rate Process written by Lech A. Grzelak and published by . This book was released on 2014 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an extension of stochastic volatility equity models by a stochastic Hull-White interest rate component while assuming non-zero correlations between the underlying processes. We place these systems of stochastic differential equations in the class of affine jump diffusion - linear quadratic jump-diffusion processes (Duffie, Pan and Singleton, Cheng and Scaillet) so that the pricing of European products can be efficiently done within the Fourier cosine expansion pricing framework. We compare the new stochastic volatility Schobel-Zhu-Hull-White hybrid model with a Heston-Hull-White model, and also apply the models to price some hybrid structured derivatives that combine the equity and interest rate asset classes.

Markov-functional and Stochastic Volatility Modelling

Author : Duy Pham
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (857 download)

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Book Synopsis Markov-functional and Stochastic Volatility Modelling by : Duy Pham

Download or read book Markov-functional and Stochastic Volatility Modelling written by Duy Pham and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study two practical problems in applied mathematical fi nance. The first topic discusses the issue of pricing and hedging Bermudan swaptions within a one factor Markov-functional model. We focus on the implications for hedging of the choice of instantaneous volatility for the one-dimensional driving Markov process of the model. We find that there is a strong evidence in favour of what we term \parametrization by time" as opposed to \parametrization by expiry". We further propose a new parametrization by time for the driving process which takes as inputs into the model the market correlations of relevant swap rates. We show that the new driving process enables a very effective vega-delta hedge with a much more stable gamma profile for the hedging portfolio compared with the existing ones. The second part of the thesis mainly addresses the topic of pricing European options within the popular stochastic volatility SABR model and its extension with mean reversion. We investigate some effcient approximations for these models to be used in real time. We first derive a probabilistic approximation for three different versions of the SABR model: Normal, Log-Normal and a displaced diffusion version for the general constant elasticity of variance case. Specifically, we focus on capturing the terminal distribution of the underlying process (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a variety of parameters which cover long dated options and highly stress market condition. This is a different feature from other current approaches which rely on the assumption of very small total volatility and usually fail for longer than 10 years maturity or large volatility of volatility. A similar study is done for the extension of the SABR model with mean reversion (SABR-MR). We first compare the SABR model with this extended model in terms of forward volatility to point out the fundamental difference in the dynamics of the two models. This is done through a numerical example of pricing forward start options. We then derive an effcient probabilistic approximation for the SABRMR model to price European options in a similar fashion to the one for the SABR model. The numerical results are shown to be still satisfactory for a wide range of market conditions.

Hedging in the Possible Presence of Unspanned Stochastic Volatility

Author : Rong Fan
Publisher :
ISBN 13 :
Total Pages : 34 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Hedging in the Possible Presence of Unspanned Stochastic Volatility by : Rong Fan

Download or read book Hedging in the Possible Presence of Unspanned Stochastic Volatility written by Rong Fan and published by . This book was released on 2002 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper examines whether higher order multifactor models, with state variables linked solely to the full set of underlying LIBOR-swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the underlying LIBOR-swap market.

Extension of Stocharstic Volatility Models with Hull-White Interest Rate Process

Author : L.A. Grzelak
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (213 download)

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Book Synopsis Extension of Stocharstic Volatility Models with Hull-White Interest Rate Process by : L.A. Grzelak

Download or read book Extension of Stocharstic Volatility Models with Hull-White Interest Rate Process written by L.A. Grzelak and published by . This book was released on 2008 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Systems in Finance and Econometrics

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
ISBN 13 : 1441977007
Total Pages : 919 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Complex Systems in Finance and Econometrics by : Robert A. Meyers

Download or read book Complex Systems in Finance and Econometrics written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.

XVA

Author : Andrew Green
Publisher : John Wiley & Sons
ISBN 13 : 1118556763
Total Pages : 548 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis XVA by : Andrew Green

Download or read book XVA written by Andrew Green and published by John Wiley & Sons. This book was released on 2015-10-08 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thorough, accessible coverage of the key issues in XVA XVA – Credit, Funding and Capital Valuation Adjustments provides specialists and non-specialists alike with an up-to-date and comprehensive treatment of Credit, Debit, Funding, Capital and Margin Valuation Adjustment (CVA, DVA, FVA, KVA and MVA), including modelling frameworks as well as broader IT engineering challenges. Written by an industry expert, this book navigates you through the complexities of XVA, discussing in detail the very latest developments in valuation adjustments including the impact of regulatory capital and margin requirements arising from CCPs and bilateral initial margin. The book presents a unified approach to modelling valuation adjustments including credit risk, funding and regulatory effects. The practical implementation of XVA models using Monte Carlo techniques is also central to the book. You'll also find thorough coverage of how XVA sensitivities can be accurately measured, the technological challenges presented by XVA, the use of grid computing on CPU and GPU platforms, the management of data, and how the regulatory framework introduced under Basel III presents massive implications for the finance industry. Explores how XVA models have developed in the aftermath of the credit crisis The only text to focus on the XVA adjustments rather than the broader topic of counterparty risk. Covers regulatory change since the credit crisis including Basel III and the impact regulation has had on the pricing of derivatives. Covers the very latest valuation adjustments, KVA and MVA. The author is a regular speaker and trainer at industry events, including WBS training, Marcus Evans, ICBI, Infoline and RISK If you're a quantitative analyst, trader, banking manager, risk manager, finance and audit professional, academic or student looking to expand your knowledge of XVA, this book has you covered.

Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models

Author : Anatoliy V. Swishchuk
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models by : Anatoliy V. Swishchuk

Download or read book Variance and Volatility Swaps and Futures Pricing for Stochastic Volatility Models written by Anatoliy V. Swishchuk and published by . This book was released on 2017 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we consider volatility swap, variance swap and VIX future pricing under different stochastic volatility models and jump diffusion models which are commonly used in financial market. We use convexity correction approximation technique and Laplace transform method to evaluate volatility strikes and estimate VIX future prices. In empirical study, we use Markov chain Monte Carlo algorithm for model calibration based on S&P 500 historical data, evaluate the effect of adding jumps into asset price processes on volatility derivatives pricing, and compare the performance of different pricing approaches.