Multiple Time Scales Stochastic Volatility Modeling Method In Heath Jarrow Morton Model Of Interest Rate Market PDF Download
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| Author | : Feiyue Di |
| Publisher | : |
| Total Pages | : 123 |
| Release | : 2011 |
| Genre | : |
| ISBN | : 9781124773117 |
Download Multiple Time Scales Stochastic Volatility Modeling Method in Heath-jarrow-morton Model of Interest Rate Market Book in PDF, ePub and Kindle
We utilize multiple time scales processes in consistent dynamic modeling to capture main time scales and heterogeneity features of the volatility process of Heath-Jarrow-Moton models in the fixed income market. The Black-Scholes type HJM models are prevailing in both industry and academy. However since these models assume that the volatility process of the underlying financial contract is constant during the term period, they are not able to incorporate some implied volatility phenomenons emerging after the Crash of 1987. Stochastic volatility modeling is one of the main approach to overcome the above defects of the Black-Scholes type models. By applying the time scale separation, that is, the singular perturbation method, we show that the stochastic volatility HJM model we proposed are parsimonious and robust effective models. In fact, we carry out this framework on the linear finite dimensional realizable HJM models, derive the explicit pricing formulas of floorlet contracts under this stochastic volatility HJM models and estimate the accuracy of the result. Meanwhile, as a specific example, we studied the stochastic volatility Hull-White model explicitly. Besides the pricing function of the floorlet contracts, we also obtain the explicit form of the pricing function of the swaption. Following the calibration procedures we proposed, we calibrated this model by a group of daily swaption data from PIMCO. The calibration result shows that the mutliple time scales stochastic volatility Hull-White model is able to capture the implied volatility smile and this model is stable statically.
| Author | : Fan Wang |
| Publisher | : |
| Total Pages | : 112 |
| Release | : 2013 |
| Genre | : |
| ISBN | : 9781303065750 |
Download Multiple Time Scales Stochastic Volatility Modeling Method in Stochastic Local Volatility Model Calibration Book in PDF, ePub and Kindle
In this thesis we study carefully the stochastic local volatility (SLV) model for pricing barrier options in foreign exchange or equity market. We first discuss the advantage and disadvantage of popular models such as stochastic volatility and local volatility that have been used for pricing the same products, then introduce the necessities to build a hybrid SLV model. We classified the calibration process of SLV model into two major parts according to parameters' different nature, and point out the slowness of the calibration procedure is mainly caused by solving the lever-age surface from Kolmogorov forward equation via the iteration method. Our major contribution is to apply the fast mean reversion volatility modeling technique and singular/regular perturbation analysis developed by Fouque, Papanicolaou, Sircar and Sølna in [24, 27, 26] to the forward equation, which gives a starting point which is proved to be close to the true solution, so that the iteration time is significantly reduced. Besides, we developed target functions specifically designed for processing exotic option quotes and give suitable numerical methods for each step of the calibration.
| Author | : P. C. G. Vassiliou |
| Publisher | : Wiley-ISTE |
| Total Pages | : 0 |
| Release | : 2014-07-08 |
| Genre | : Mathematics |
| ISBN | : 9781848211599 |
Download Continuous-time Asset Pricing Models in Applied Stochastic Finance Book in PDF, ePub and Kindle
Stochastic finance and financial engineering have been rapidly expanding fields of science over the past four decades, mainly due to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging this kind of risk. These two volumes aim to provide a foundation course on applied stochastic finance. They are designed for three groups of readers: firstly, students of various backgrounds seeking a core knowledge on the subject of stochastic finance; secondly financial analysts and practitioners in the investment, banking and insurance industries; and finally other professionals who are interested in learning advanced mathematical and stochastic methods, which are basic knowledge in many areas, through finance. In Volume 2 we study continuous time models by presenting the necessary material from continuous martingales, measure theory and stochastic differential equations as models for various assets, such as the Wiener process, Brownian motion, etc. We then build, with many examples and intuitive explanations, the necessary stochastic analysis background i.e. Itô’s lemma, stochastic integration, Girsanovís theorem, etc. The book then guides the reader into the pricing of vanilla options in continuous time i.e. the continuous time models of Black and Scholes, followed by interest rate models and the models of Heath-Jarrow-Morton and the forward Libor model. The final part of the book presents the pricing of credit derivatives.
| Author | : Josep Perelló |
| Publisher | : |
| Total Pages | : 19 |
| Release | : 2013 |
| Genre | : |
| ISBN | : |
Download Multiple Time Scales in Volatility and Leverage Correlations Book in PDF, ePub and Kindle
Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or 'leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. We extend the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. We find that the resulting three-dimensional diffusion process can account for different correlation time scales. We show that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days.
| Author | : Marek Musiela |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 721 |
| Release | : 2006-01-20 |
| Genre | : Mathematics |
| ISBN | : 3540266534 |
Download Martingale Methods in Financial Modelling Book in PDF, ePub and Kindle
A new edition of a successful, well-established book that provides the reader with a text focused on practical rather than theoretical aspects of financial modelling Includes a new chapter devoted to volatility risk The theme of stochastic volatility reappears systematically and has been revised fundamentally, presenting a much more detailed analyses of interest-rate models
| Author | : Mitchell Craig Warachka |
| Publisher | : Ann Arbor, Mich. : University Microfilms International |
| Total Pages | : 318 |
| Release | : 2000 |
| Genre | : |
| ISBN | : |
Download Incorporating Stochastic Volatility Into the Heath, Jarrow, and Morton Term Structure Model Book in PDF, ePub and Kindle
| Author | : Peter H. Rossi |
| Publisher | : Elsevier |
| Total Pages | : 505 |
| Release | : 1996-11-19 |
| Genre | : Business & Economics |
| ISBN | : 0080511872 |
Download Modelling Stock Market Volatility Book in PDF, ePub and Kindle
This essay collection focuses on the relationship between continuous time models and Autoregressive Conditionally Heteroskedastic (ARCH) models and applications. For the first time, Modelling Stock Market Volatility provides new insights about the links between these two models and new work on practical estimation methods for continuous time models. Featuring the pioneering scholarship of Daniel Nelson, the text presents research about the discrete time model, continuous time limits and optimal filtering of ARCH models, and the specification and estimation of continuous time processes. This work will lead to a rapid growth in their empirical application as they are increasingly subjected to routine specification testing. Provides for the first time new insights on the links between continuous time and ARCH models Collects seminal scholarship by some of the most renowned researchers in finance and econometrics Captures complex arguments underlying the approximation and proper statistical modelling of continuous time volatility dynamics
| 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 | : Nicolas Privault |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 191 |
| Release | : 2008-10-13 |
| Genre | : Business & Economics |
| ISBN | : 9813107308 |
Download An Elementary Introduction To Stochastic Interest Rate Modeling Book in PDF, ePub and Kindle
This textbook is written as an accessible introduction to interest rate modeling and related derivatives, which have become increasingly important subjects of interest in financial mathematics. The models considered range from standard short rate to forward rate models and include more advanced topics such as the BGM model and an approach to its calibration. An elementary treatment of the pricing of caps and swaptions under forward measures is also provided, with a focus on explicit calculations and a step-by-step introduction of concepts. Each chapter is accompanied with exercises and their complete solutions, making this book suitable for advanced undergraduate or beginning graduate-level students.
| Author | : Anjun Zhou |
| Publisher | : |
| Total Pages | : 36 |
| Release | : 2000 |
| Genre | : |
| ISBN | : |
Download Modeling the Volatility of the Heath-Jarrow-Morton Model Book in PDF, ePub and Kindle
Based on the nonparametric study of Pearson and Zhou (1999), a parametric HJM model is developed for the forward rate volatility. It allows the volatility of the forward rate with different maturities to react in a different way with the level of forward rate and the forward spread. Specifically, the proposed forward rate volatility function is imbedded into GARCH family models and compared with several widely used HJM volatility specifications. It is shown that the proposed volatility specification performs the best. It is also confirmed that the volatility of forward rate with different maturities depends on the forward rate and the forward spread in a different way.
