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Author : Stanley Mathew
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (423 download)
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 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jianwei Zhu
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (129 download)
Download or read book An Extended Libor Market Model With Nested Stochastic Volatility Dynamics written by Jianwei Zhu and published by . This book was released on 2007 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend standard Libor Market Model (LMM) with nested stochastic volatilities. The stochastic volatility of each Libor follows a mean-reverting process as in Schoebel and Zhu (1999) or in Heston (1993) under the individual forward measure of each Libor. Other than the existing stochastic volatility models, every volatility in the extended LMM is correlated with its Libor individually, and the parameters of stochastic volatility are also different over all Libors, however, are nested by some deterministic functions. With a nesting function, the same type of parameter such as mean level in all volatility processes share a certain term structure. In this model set-up, we can still derive the stochastic processes for Libors and volatilities under an arbitrary forward measure. In line with the stochastic volatility models for equity options, we obtain a closed-form solution via Fourier transform for caplets and floorlets. Finally, we use factor representation to express Libors and swap rates by some independent factors, namely principle components. The approximated analytical pricing formula principal for swaption can then be derived by using the characteristic functions that are just a product of the characteristic function of each factor. The numerical implementation of the nested stochastic volatility model is efficient and identical to the existing stochastic volatility models.
Author : Dariusz Gatarek
Publisher :
ISBN 13 :
Total Pages : 8 pages
Book Rating : 4.:/5 (129 download)
Download or read book Libor Market Model with Stochastic Volatility written by Dariusz Gatarek and published by . This book was released on 2003 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Four papers introducing LIBOR market model (LMM) were published in 1997. They seemed to unify market practice with arbitrage-free framework - it came out that for one year only. The next year, after Russian crisis, cap and swaption markets started to show evident volatility smile and skew. Several attempts were made to capture that phenomenon into the arbitrage-free framework. Our note is strongly inspired by papers and conference talks by Mark Joshi and Riccardo Rebonato. We share their opinions that:- Since smiles and skews are caused by different market features, it is more natural to model smile and skew separately, rather then to use unified framework of implied smile.- Displaced Diffusion approach is easier in treatment then Constant Elasticity of Variance (CEV) approach for interest rate derivatives and gives the same modelling possibilities.- Displaced Diffusion and Stochastic Volatility are perfectly suited to work together.Since our attention is fixed more on swaptions then on caps/floors, we would like to opt for another version of the LIBOR market model with stochastic volatility and displaced diffusion (SVDDLMM) then Joshi and Rebonato:- We use various random displacement factors for various LIBOR rates. - For Stochastic Volatility we propose a new simple non mean reverting multi-lognormal model. We also try to convince the Reader that mean reversion in stochastic volatility models excludes correct modelling of long term options - swaptions are canonical example.Easy closed form formulae are given for caps/floors and European swaptions what makes calibration procedure more effective and transparent - at least we are not quot;prisoners of Monte Carloquot;. We are able to calibrate model to various smile/skew shapes for caps/floors and swaptions with various length and of various maturities.
Author : Lech A. Grzelak
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.:/5 (13 download)
Download or read book On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates 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 construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull-White [HW96]. We then extend the framework by modeling the interest rate by a stochastic volatility displaced-diffusion Libor Market Model [AA02], which can model an interest rate smile. We provide semi-closed form approximations which lead to efficient calibration of the multi-currency models. Finally, we add a correlated stock to the framework and discuss the construction, model calibration and pricing of equity-FX-interest rate hybrid payoffs.
Author : Leif B. G. Andersen
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (129 download)
Download or read book Extended Libor Market Models with Stochastic Volatility written by Leif B. G. Andersen and published by . This book was released on 2002 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces stochastic volatility to the Libor market model of interest rate dynamics. As in Andersen and Andreasen (2000a) we allow for non-parametric volatility structures with freely specifiable level dependence (such as, but not limited to, the CEV formulation), but now also include a multiplicative perturbation of the forward volatility surface by a general mean-reverting stochastic volatility process. The resulting model dynamics allow for modeling of non-monotonic volatility smiles while explicitly allowing for control of the stationarity properties of the resulting model dynamics. Using asymptotic expansion techniques, we provide closed-form pricing formulas for caps and swaptions that are robust, accurate, and well-suited for both model calibration and general mark-to-market of plain-vanilla instruments. Monte Carlo schemes for the proposed model are proposed and examined.
Author : Daniel Thunbo
Publisher :
ISBN 13 :
Total Pages : 123 pages
Book Rating : 4.:/5 (488 download)
Download or read book LIBOR Market Models with Stochastic Volatility written by Daniel Thunbo and published by . This book was released on 2008 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christoph Hackl
Publisher : Springer Science & Business Media
ISBN 13 : 3658046880
Total Pages : 69 pages
Book Rating : 4.6/5 (58 download)
Download or read book Calibration and Parameterization Methods for the Libor Market Model written by Christoph Hackl and published by Springer Science & Business Media. This book was released on 2013-12-27 with total page 69 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Libor Market Model (LMM) is a mathematical model for pricing and risk management of interest rate derivatives and has been built on the framework of modelling forward rates. For the conceptual understanding of the model a strong background in the fields of mathematics, statistics, finance and especially for implementation, computer science is necessary. The book provides the ne cessary groundwork to understand the LMM and delivers a framework to implement a working model where possible calibration and parameterization methods for volatility and correlation are explained. Special emphasis lies also on the trade off of speed and correctness where differences in choosing random number generators and the advantages of factor reduction are shown.
Download or read book A Stochastic Volatility LIBOR Market Model with a Closed Form Solution written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shengqiang Xu
Publisher :
ISBN 13 :
Total Pages : 272 pages
Book Rating : 4.:/5 (857 download)
Download or read book A Multi-curve Libor Market Model with Uncertainties Described by Random Fields written by Shengqiang Xu and published by . This book was released on 2012 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Cornelis W Oosterlee
Publisher : World Scientific
ISBN 13 : 1786347962
Total Pages : 1310 pages
Book Rating : 4.7/5 (863 download)
Download or read book Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes written by Cornelis W Oosterlee and published by World Scientific. This book was released on 2019-10-29 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.Supplementary Material:Solutions Manual is available to instructors who adopt this textbook for their courses. Please contact [email protected].
Author : Kenjiro Oya
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (13 download)
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.
Author : Osamu Tsuchiya
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (13 download)
Download or read book Markovian Projection for the Local Stochastic Volatility Libor Market Model written by Osamu Tsuchiya and published by . This book was released on 2015 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Markovian Projection is investigated for the Local Stochastic Volatility Libor Market Model. An approximation based on the Log Normal process is introduced. In this approximation, the Markovian Projection is fitted to the CEV model rather than to Displaced Diffusion. The relationship with a Standard Method is also investigated.
Author : Matthias Lutz
Publisher :
ISBN 13 :
Total Pages : 175 pages
Book Rating : 4.:/5 (753 download)
Download or read book Libor Market Models with Stochastic Volatility and CMS Spread Option Pricing written by Matthias Lutz and published by . This book was released on 2011 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Benner
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book A Multi-Factor Cross-Currency LIBOR Market Model written by Wolfgang Benner and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a rigorous two-currency pricing framework that can be constructed under either a domestic or a foreign currency numeraire. While plain vanilla interest rate derivative prices are recovered by design, exotic cross-currency interest rate products can be priced by determining no-arbitrage drifts for both the domestic and the foreign LIBORs under a uniform probability measure and by specifying the dynamics of the domestic and foreign currency leg of the exotic product. In a single-currency world, no-arbitrage drifts can always be found by specifying the evolution of the terminal LIBOR as a function of bond price volatilities, first, and solving for the drifts of all remaining LIBORs by backward induction. After introducing a second currency, we show that traditional backward induction for the second currency must fail due to interdependence between the respective bond price volatilities and LIBOR dynamics. In order to resolve any such interdependence, we propose calibrating the volatility function of the spot exchange rate to the terminal maturity spectrum of FX options and specifying a functional form for all dates prior to the terminal one. By choosing a multi-factor model setup, rather than relying on terminal decorrelation within a single-factor model, we allow for model calibration to an exogenous market correlation mix. Extending the model, we outline modifications to account for volatility skews by introducing displaced-diffusion to the LIBOR and FX rate dynamics.
Author : Chi Kwong Au
Publisher :
ISBN 13 :
Total Pages : 80 pages
Book Rating : 4.:/5 (311 download)
Download or read book Instant Calibration to the Stochastic Volatility LIBOR Market Model written by Chi Kwong Au and published by . This book was released on 2008 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christian Zühlsdorff
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (129 download)
Download or read book Extended Libor Market Models with Affine and Quadratic Volatility written by Christian Zühlsdorff and published by . This book was released on 2000 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The market model of interest rates specifies simple forward or LIBOR rates as lognormaly distributed, their stochastic dynamics has a linear volatility function. This model is extended to quadratic volatility which is the product of a quadratic polynomial and a level-independent covariance matrix. I derive extensions of the Black cap pricing formula in this setup and give examples for the possible shapes of implied volatilities. Then I give a new approximative swaption pricing formula and discuss the goodness of the approximation. The model is calibrated to market prices, it shows no extended model specification outperforms the others. The criteria for model choice should thus be theoretical properties and computational efficiency.
Author : Giorgio Mori
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (13 download)
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.
