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Exact Solution To Cev Model With Uncorrelated Stochastic Volatility
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Book Synopsis Exact Solution to CEV Model with Uncorrelated Stochastic Volatility by : Alexandre Antonov
Download or read book Exact Solution to CEV Model with Uncorrelated Stochastic Volatility written by Alexandre Antonov and published by . This book was released on 2014 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility models are widely used in interest rate modeling to match the option smiles -- the two most popular are the Heston model and the SABR one. These have been incorporated into arbitrage-free term structure frameworks, Heston-LMM and SABR-LMM respectively.In this paper we consider the CEV model with a general stochastic volatility. Assuming that rate-volatility correlation is zero we are able to obtain an exact integral representation of the option price provided that we have a closed form for a Moment Generating Function of the cumulative stochastic variance or of its inverse. Using this result we derive explicit solutions in terms of two-dimensional integral for both CEV-CIR model (or power generalization of the Heston) and the SABR one. Moreover the results in this paper may be easily extended to any affine process (possibly multi-factor and including jumps) leading to numerous practical applications.
Book Synopsis A Simple Approach to the Estimation of Continuous Time CEV Stochastic Volatility Models of the Short-term Rate by : Fabio Fornari
Download or read book A Simple Approach to the Estimation of Continuous Time CEV Stochastic Volatility Models of the Short-term Rate written by Fabio Fornari and published by . This book was released on 2001 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Comparison of Biased Simulation Schemes for Stochastic Volatility Models by : Roger Lord
Download or read book A Comparison of Biased Simulation Schemes for Stochastic Volatility Models written by Roger Lord and published by . This book was released on 2008 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an Euler discretisation to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the CEV-SV stochastic volatility model, with the Heston model as a special case, where the variance is modelled as a mean-reverting CEV process. Consequently, when using an Euler discretisation, one must carefully think about how to fix negative variances. Our contribution is threefold. Firstly, we unify all Euler fixes into a single general framework. Secondly, we introduce the new full truncation scheme, tailored to minimise the positive bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to recent quasi-second order schemes of Kahl and Jauml;ckel and Ninomiya and Victoir, as well as to the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme outperforms all considered biased schemes in terms of bias and root-mean-squared error.
Book Synopsis Analysis, Geometry, and Modeling in Finance by : Pierre Henry-Labordere
Download or read book Analysis, Geometry, and Modeling in Finance written by Pierre Henry-Labordere and published by CRC Press. This book was released on 2008-09-22 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th
Book Synopsis A SIMPLE APPROACH TO THE ESTIMATION OF CONTINUOIS TIME CEV STOCHASTIC VOLATILITY MODELS OF THE SHORT-TERM RATE by : Fabio FORNARI
Download or read book A SIMPLE APPROACH TO THE ESTIMATION OF CONTINUOIS TIME CEV STOCHASTIC VOLATILITY MODELS OF THE SHORT-TERM RATE written by Fabio FORNARI and published by . This book was released on 2001 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis VIX Derivatives Valuation and Estimation Based on Closed-Form Series Expansions by : Zhe Zhao
Download or read book VIX Derivatives Valuation and Estimation Based on Closed-Form Series Expansions written by Zhe Zhao and published by . This book was released on 2018 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new valuation and calibration method for VIX futures and VIX options is proposed. The method is based on a closed-form Hermite series expansion for a stochastic volatility model with the stochastic variance process driven by an affine drift term. We implement the methodology for the Heston and the mean-reverting CEV stochastic volatility models. A calibration exercise to real market data shows that the method is efficient, accurate, and suitable for practical implementation.
Download or read book Monte Carlo written by George Fishman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: Apart from a thorough exploration of all the important concepts, this volume includes over 75 algorithms, ready for putting into practice. The book also contains numerous hands-on implementations of selected algorithms to demonstrate applications in realistic settings. Readers are assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained. Suitable for graduates and undergraduates in mathematics and engineering, in particular operations research, statistics, and computer science.
Download or read book Risk written by and published by . This book was released on 2001-07 with total page 932 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Volatility and Correlation by : Riccardo Rebonato
Download or read book Volatility and Correlation written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2005-07-08 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School
Book Synopsis Designing a Simple Loss Function for Central Banks by : Davide Debortoli
Download or read book Designing a Simple Loss Function for Central Banks written by Davide Debortoli and published by International Monetary Fund. This book was released on 2017-07-21 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: Yes, it makes a lot of sense. This paper studies how to design simple loss functions for central banks, as parsimonious approximations to social welfare. We show, both analytically and quantitatively, that simple loss functions should feature a high weight on measures of economic activity, sometimes even larger than the weight on inflation. Two main factors drive our result. First, stabilizing economic activity also stabilizes other welfare relevant variables. Second, the estimated model features mitigated inflation distortions due to a low elasticity of substitution between monopolistic goods and a low interest rate sensitivity of demand. The result holds up in the presence of measurement errors, with large shocks that generate a trade-off between stabilizing inflation and resource utilization, and also when ensuring a low probability of hitting the zero lower bound on interest rates.
Book Synopsis Correlation Risk Modeling and Management by : Gunter Meissner
Download or read book Correlation Risk Modeling and Management written by Gunter Meissner and published by John Wiley & Sons. This book was released on 2013-12-19 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough guide to correlation risk and its growing importance in global financial markets Ideal for anyone studying for CFA, PRMIA, CAIA, or other certifications, Correlation Risk Modeling and Management is the first rigorous guide to the topic of correlation risk. A relatively overlooked type of risk until it caused major unexpected losses during the financial crisis of 2007 through 2009, correlation risk has become a major focus of the risk management departments in major financial institutions, particularly since Basel III specifically addressed correlation risk with new regulations. This offers a rigorous explanation of the topic, revealing new and updated approaches to modelling and risk managing correlation risk. Offers comprehensive coverage of a topic of increasing importance in the financial world Includes the Basel III correlation framework Features interactive models in Excel/VBA, an accompanying website with further materials, and problems and questions at the end of each chapter
Book Synopsis Modern SABR Analytics by : Alexandre Antonov
Download or read book Modern SABR Analytics written by Alexandre Antonov and published by Springer. This book was released on 2019-05-02 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.
Book Synopsis Stochastic Calculus for Fractional Brownian Motion and Applications by : Francesca Biagini
Download or read book Stochastic Calculus for Fractional Brownian Motion and Applications written by Francesca Biagini and published by Springer Science & Business Media. This book was released on 2008-02-17 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.
Book Synopsis Technology Shocks and Aggregate Fluctuations by : Mr.Pau Rabanal
Download or read book Technology Shocks and Aggregate Fluctuations written by Mr.Pau Rabanal and published by International Monetary Fund. This book was released on 2004-12-01 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our answer: Not so well. We reached that conclusion after reviewing recent research on the role of technology as a source of economic fluctuations. The bulk of the evidence suggests a limited role for aggregate technology shocks, pointing instead to demand factors as the main force behind the strong positive comovement between output and labor input measures.
Book Synopsis SABR and SABR LIBOR Market Models in Practice by : Christian Crispoldi
Download or read book SABR and SABR LIBOR Market Models in Practice written by Christian Crispoldi and published by Springer. This book was released on 2016-04-29 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest rate traders have been using the SABR model to price vanilla products for more than a decade. However this model suffers however from a severe limitation: its inability to value exotic products. A term structure model à la LIBOR Market Model (LMM) is often employed to value these more complex derivatives, however the LMM is unable to capture the volatility smile. A joint SABR LIBOR Market Model is the natural evolution towards a consistent pricing of vanilla and exotic products. Knowledge of these models is essential to all aspiring interest rate quants, traders and risk managers, as well an understanding of their failings and alternatives. SABR and SABR Libor Market Models in Practice is an accessible guide to modern interest rate modelling. Rather than covering an array of models which are seldom used in practice, it focuses on the SABR model, the market standard for vanilla products, the LIBOR Market Model, the most commonly used model for exotic products and the extended SABR LIBOR Market Model. The book takes a hands-on approach, demonstrating simply how to implement and work with these models in a market setting. It bridges the gap between the understanding of the models from a conceptual and mathematical perspective and the actual implementation by supplementing the interest rate theory with modelling specific, practical code examples written in Python.
Book Synopsis A Practical Guide to Forecasting Financial Market Volatility by : Ser-Huang Poon
Download or read book A Practical Guide to Forecasting Financial Market Volatility written by Ser-Huang Poon and published by John Wiley & Sons. This book was released on 2005-08-19 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial market volatility forecasting is one of today's most important areas of expertise for professionals and academics in investment, option pricing, and financial market regulation. While many books address financial market modelling, no single book is devoted primarily to the exploration of volatility forecasting and the practical use of forecasting models. A Practical Guide to Forecasting Financial Market Volatility provides practical guidance on this vital topic through an in-depth examination of a range of popular forecasting models. Details are provided on proven techniques for building volatility models, with guide-lines for actually using them in forecasting applications.
Book Synopsis Interest Rate Models - Theory and Practice by : Damiano Brigo
Download or read book Interest Rate Models - Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
