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.

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

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.

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.

Download or read book A Hybrid Stochastic Volatility Model Incorporating Local Volatility written by Yu Tian and published by . This book was released on 2014 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present our study on a hybrid stochastic volatility model incorporating local volatility for pricing options in the foreign exchange (FX) market. The hybrid stochastic-local volatility model (SLV) could match the implied volatility surface well and meanwhile shows the flexibility for pricing exotic options. The difficulty in implementing the SLV model lies in the calibration of the leverage function, which can be roughly seen as a ratio between the local volatility and the conditional expectation of stochastic volatility. We will illustrate our implementation of the SLV model and show the pricing performance for exotic options.

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.

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.

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by . This book was released on 2016 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Chapter 2 of Stochastic Volatility Modeling, published by CRC/Chapman & Hall.In this chapter the local volatility model is surveyed as a market model for the underlying together with its associated vanilla options.First, relationships of implied to local volatilities are derived, as well as approximations for skew and curvature. Exact and approximate techniques for taking dividends into account are presented.We then turn to the dynamics of the local volatility model. We introduce the Skew Tickiness Ratio (SSR) and derive approximate formulas for the SSR and volatilities of volatilities in the local volatility model.We also examine future skews.We then consider the delta and carry P&L of a hedged option position. We derive the expression of the market-model delta of the local volatility model and discuss the relationship between sticky-strike and market-model deltas. We characterize the gamma/theta break-even levels of a hedged position and show that the local volatility model is indeed a market model.We then derive the expression of the vega-hedge portfolio.Markov-functional models are considered next.Finally, we survey the Uncertain Volatility Model and its usage.A digest summarizes key points.

Download or read book Market Practice In Financial Modelling written by Chia Chiang Tan and published by World Scientific Publishing Company. This book was released on 2012-07-11 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written to bridge the gap between foundational quantitative finance and market practice, this book goes beyond the basics covered in most textbooks by presenting content concerning actual industry norms, thus resulting in a clearer picture of the field for the readers. These include, for instance, the practitioner's perspective of how local versus stochastic volatility affects forward smile, or the implications of mean reversion on forward volatility.Key considerations for modelling in rates, equities and foreign exchange are presented from the perspective of common themes across various assets, as well as their individual characteristics.The discussion on models emphasizes the key aspects that are relevant to the pricing of different types of financial derivatives, so that the reader can observe how an appropriate choice of models is essential in reflecting the risk profile and hedging considerations for different products.With the knowledge gleaned from this book, readers will attain a more comprehensive understanding of market practice in derivatives modelling.

Download or read book The Hybrid Stochastic Local Volatility Model with Applications in Pricing FX Options written by Yu Tian and published by . This book was released on 2016 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. On the other hand, the local volatility model can reproduce the implied volatility surface, whereas it does not consider the stochastic behaviour of the volatility. To combine the advantages of stochastic volatility (SV) and local volatility (LV) models, a class of stochastic-local volatility (SLV) models has been developed. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In the thesis, we first review the fundamental theories of stochastic differential equations and the classic option pricing models, and study the behaviour of the volatility in the context of FX market. We then introduce the SLV model and illustrate our implementation of the calibration and pricing procedure. We apply the SLV model to exotic option pricing in the FX market and compare pricing results of the SLV model with pure local volatility and pure stochastic volatility models. Numerical results show that the SLV model can match the implied volatility surface very well as well as improve the pricing performance for barrier options. In addition, we further discuss some extensions of the SLV project, such as parallelization potential for accelerating option pricing and pricing techniques for window barrier options. Although the SLV model we use in the thesis is not entirely new, we contribute to the research in the following aspects: 1) we investigate the hybrid volatility modeling thoroughly from theoretical backgrounds to practical implementations; 2) we resolve some critical issues in implementing the SLV model such as developing a fast and stable numerical method to derive the leverage function; and 3) we build a robust calibration and pricing platform under the SLV model, which can be extended for practical uses.

Download or read book Advanced Equity Derivatives written by Sebastien Bossu and published by John Wiley & Sons. This book was released on 2014-05-19 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Advanced Equity Derivatives: Volatility and Correlation, Sébastien Bossu reviews and explains the advanced concepts used for pricing and hedging equity exotic derivatives. Designed for financial modelers, option traders and sophisticated investors, the content covers the most important theoretical and practical extensions of the Black-Scholes model. Each chapter includes numerous illustrations and a short selection of problems, covering key topics such as implied volatility surface models, pricing with implied distributions, local volatility models, volatility derivatives, correlation measures, correlation trading, local correlation models and stochastic correlation. The author has a dual professional and academic background, making Advanced Equity Derivatives: Volatility and Correlation the perfect reference for quantitative researchers and mathematically savvy finance professionals looking to acquire an in-depth understanding of equity exotic derivatives pricing and hedging.

Download or read book Local Stochastic Volatility Models written by Cristian Homescu and published by . This book was released on 2014 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze in detail calibration and pricing performed within the framework of local stochastic volatility LSV models, which have become the industry market standard for FX and equity markets. We present the main arguments for the need of having such models, and address the question whether jumps have to be included. We include a comprehensive literature overview, and focus our exposition on important details related to calibration procedures and option pricing using PDEs or PIDEs derived from LSV models. We describe calibration procedures, with special attention given to usage and solution of corresponding forward Kolmogorov PDE/PIDE, and outline powerful algorithms for estimation of model parameters. Emphasis is placed on presenting practical details regarding the setup and the numerical solution of both forward and backward PDEs/PIDEs obtained from the LSV models. Consequently we discuss specifics (based on our experience and best practices from literature) regarding choice of boundary conditions, construction of nonuniform spatial grids and adaptive temporal grids, selection of efficient and appropriate finite difference schemes (with possible enhancements), etc. We also show how to practically integrate specific features of various types of financial instruments within calibration and pricing settings. We consider all questions and topics identified as most relevant during the selection, calibration and pricing procedures associated with local stochastic volatility models, providing answers (to the best of our knowledge), and present references for deeper understanding and for additional perspectives. In a nutshell, it is our intention to present here an effective roadmap for a successful LSV journey.

Download or read book Turbo Charged Local Stochastic Volatility Models written by Ghislain Vong and published by . This book was released on 2013 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article presents an alternative formulation of the standard Local Stochastic Volatility model (LSV) widely used for the pricing and risk-management of FX derivatives and to a lesser extent of equity derivatives. In the standard model, calibration is achieved by solving a non-linear two-factor Kolmogorov forward PDE, where a minimum number of vol points is required to achieve convergence of a finite difference implementation. In contrast, we propose to model the volatility process by a Markov chain defined over an arbitrary small number of states, so that calibration and pricing are achieved by solving a coupled system of one-factor PDEs. The practical benefits are twofolds: existing one-factor PDE solvers can be recycled to model stochastic volatility, while the reduction in number of discretisation points implies a speedup in execution time that enables real-time risk-management of large derivatives position.

Download or read book Volatility Surface and Term Structure written by Kin Keung Lai and published by Routledge. This book was released on 2013-09-11 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.

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.

Download or read book Topics in Volatility Models written by Cong Yi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis I will present my PhD research work, focusing mainly on financialmodelling of asset?s volatility and the pricing of contingent claims (financial derivatives), which consists of four topics:1. Several changing volatility models are introduced and the pricing of Europeanoptions is derived under these models;2. A general local stochastic volatility model with stochastic interest rates (IR)is studied in the modelling of foreign exchange (FX) rates. The pricing of FXoptions under this model is examined through the use of an asymptotic expansionmethod, based on Watanabe-Yoshida theory. The perfect/partial hedging issuesof FX options in the presence of local stochastic volatility and stochastic IRs arealso considered. Finally, the impact of stochastic volatility on the pricing of FX-IRstructured products (PRDCs) is examined;3. A new method of non-biased Monte Carlo simulation for a stochastic volatilitymodel (Heston Model) is proposed;4. The LIBOR/swap market model with stochastic volatility and jump processesis studied, as well as the pricing of interest rate options under that model. In conclusion, some future research topics are suggested. Key words: Changing Volatility Models, Stochastic Volatility Models, LocalStochastic Volatility Models, Hedging Greeks, Jump Diffusion Models, ImpliedVolatility, Fourier Transform, Asymptotic Expansion, LIBOR Market Model, MonteCarlo Simulation, Saddle Point Approximation.

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.