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Implementation Of A One Factor Markov Functional Interest Rate Model
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Book Synopsis Implementation of a One-Factor Markov-Functional Interest Rate Model by : Baptiste Truchot
Download or read book Implementation of a One-Factor Markov-Functional Interest Rate Model written by Baptiste Truchot and published by . This book was released on 2016 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest rate market has been expanding immensely for thirty years, both in term of volumes and diversity of traded contracts. The growing complexity of derivatives has implied a need for sophisticated models in order to price and hedge these products. Three main approaches can be distinguished in interest rates modeling. Short-rate models model the dynamics of the term structure of interest rates by specifying the dynamics of a single rate (the spot rate or the instantaneous spot rate) from which the whole term structure at any point in time can be calculated. The prices of derivatives in these models are quite involved functions of the underlying process which is being modeled. This fact makes these models difficult to calibrate. However the short rate process is easy to follow and hence implementation is straightforward.Unlike short rate models the class of Market Models is formulated in terms of market rates which are directly related to tradable assets. Thus they exhibit better calibration properties than short rate models. However they are high dimensional by construction and tedious to implement.In 1999, Hunt, Kennedy and Pelsser introduced the class of Markov-Functional Models (MFM) aiming at developing models which could match as many market prices as Market Models while maintaining the efficiency of short rate models in calculating derivative prices.After a general overview of the two dominant paradigms in section III, this report will focus on the class of Markov-functional models. Section IV presents the general framework. Then several issues related to the implementation of a one-factor MFM model are analyzed in section V. Finally we will display in section VI some numerical results of the simulations of this one-factor model.
Book Synopsis One-Dimensional Markov-Functional Models Driven by Non-Gaussian Markov Processes by : Jaka Gogala
Download or read book One-Dimensional Markov-Functional Models Driven by Non-Gaussian Markov Processes written by Jaka Gogala and published by . This book was released on 2017 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of Markov-functional models provide a framework that can be used to define interest-rate models of finite dimension calibrated to any arbitrage-free formula for caplet or swaption prices. Because of their computational efficiency one-factor Markov-functional models are of particular interest. So far the literature has been focused on models driven by a Gaussian process. The aim of this paper is to move away from this Gaussian assumption and to provide new algorithms that can be used to implement a Markov-functional model driven by a more general class of one-dimensional diffusion processes. We provide additional insight into the role of the driving process by presenting a simple copula-based criterion that can be used to distinguish between models. Finally we offer further insight into the dynamics of one-dimensional Markov-functional models by relating them to separable local-volatility LIBOR market models and demonstrate this with a practical example.
Book Synopsis Markov-Functional Interest Rate Models by : Phil J. Hunt
Download or read book Markov-Functional Interest Rate Models written by Phil J. Hunt and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a general class of interest rate models in which the value of pure discount bonds can be expressed as a functional of some (low-dimensional) Markov process. At the abstract level this class includes all current models of practical importance. By specifying these models in Markov-functional form, we obtain a specification which is efficient to implement. An additional advantage of Markov-functional models is the fact that the specification of the model can be such that the forward rate distribution implied by market option prices can be fitted exactly, which makes these models particularly suited for derivatives pricing. We give examples of Markov-functional models that are fitted to market prices of caps/floors and swaptions.
Book Synopsis An N-Dimensional Markov-Functional Interest Rate Model by : Linus Kaisajuntti
Download or read book An N-Dimensional Markov-Functional Interest Rate Model written by Linus Kaisajuntti and published by . This book was released on 2019 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops an n-dimensional Markov-functional interest rate model, i.e. a model driven by an n-dimensional state process and constructed using Markov-functional techniques. It is shown that this model is very similar to an n-factor LIBOR market model hence allowing intuition from the LIBOR market model to be transferred to the Markov-functional model. This generalises the results of Bennett amp;amp; Kennedy (2005) from one-dimensional to n-dimensional driving state processes. The model is suitable for pricing certain type of exotic interest rate derivative products such as TARNs on LIBORs or CMS spreads. For these products, the n-dimensional Markov-functional model may be used as a benchmark model allowing for powerful and flexible control of both correlations between different rates as well as skews/smiles in implied volatilities.
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.
Book Synopsis Efficient Methods for Valuing Interest Rate Derivatives by : Antoon Pelsser
Download or read book Efficient Methods for Valuing Interest Rate Derivatives written by Antoon Pelsser and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the models that can be used for valuing and managing interest rate derivatives. Split into two parts, the first discusses and compares the traditional models, such as spot- and forward-rate models, while the second concentrates on the more recently developed Market models. Unlike most of his competitors, the author's focus is not only on the mathematics: Antoon Pelsser draws on his experience in industry to explore a host of practical issues.
Book Synopsis Markov-functional Interest Rate Models by : Philip A. Hunt
Download or read book Markov-functional Interest Rate Models written by Philip A. Hunt and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The LIBOR Market Model in Practice by : Dariusz Gatarek
Download or read book The LIBOR Market Model in Practice written by Dariusz Gatarek and published by John Wiley & Sons. This book was released on 2007-01-30 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent with the market practice of pricing interest rate derivatives and therefore it is widely used by financial institution for valuation of interest rate derivatives. This book provides a full practitioner's approach to the LIBOR Market Model. It adopts the specific language of a quantitative analyst to the largest possible level and is one of first books on the subject written entirely by quants. The book is divided into three parts - theory, calibration and simulation. New and important issues are covered, such as various drift approximations, various parametric and nonparametric calibrations, and the uncertain volatility approach to smile modelling; a version of the HJM model based on market observables and the duality between BGM and HJM models. Co-authored by Dariusz Gatarek, the 'G' in the BGM model who is internationally known for his work on LIBOR market models, this book offers an essential perspective on the global benchmark for short-term interest rates.
Book Synopsis A Two-Factor Markov Functional Model by : Frank Genheimer
Download or read book A Two-Factor Markov Functional Model written by Frank Genheimer and published by . This book was released on 2003 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cross-Currency and Hybrid Markov-Functional Models by : Christian P. Fries
Download or read book Cross-Currency and Hybrid Markov-Functional Models written by Christian P. Fries and published by . This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider cross-currency Markov-functional models and their calibration under the spot measure. Hunt, Kennedy and Pelsser introduced a single-currency Markov-functional interest rate model in the terminal measure and showed how to efficiently calibrate it to LIBOR or swaprate options. Building upon their work we will present a multi-factor cross-currency LIBOR model under different measures. We see zero correlated FX spot and LIBOR rates as a natural starting point. Under this assumption we don't need a change of numeraire drift correction and the functionals of the foreign currency rates under the domestic numeraire are identical to the functionals of the foreign currency model under its (foreign) spot measure. This provides the motivation for first deriving a spot measure version of single-currency Markov-functional model. We will show that in the spot measure it is possible to formulate and implement a very efficient calibration procedure comparable to that provided by Hunt, Kennedy and Pelsser for the terminal measure. Combining single-currency Markov-functional interest rate models with a Markov-functional FX spot model we build two and three factor cross-currency models. Relaxing the zero correlation assumption is technically quite simple, but it entails considerable additional computational costs, mainly for the calibration of the model to FX options. To circumvent this problem we suggest a more efficient approximate procedure, which seems to work quite well for low correlations.
Book Synopsis Longstaff-Schwartz, Effective Model Dimensionality and Reducible Markov-Functional Models by : Phil J. Hunt
Download or read book Longstaff-Schwartz, Effective Model Dimensionality and Reducible Markov-Functional Models written by Phil J. Hunt and published by . This book was released on 2005 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The popularity of the so-called Market Models has led researchers and practitioners to ask two important questions about modelling interest-rate derivatives. The first (and highly contentious) question is, how many stochastic drivers are needed to value accurately any given derivative? The second, which arises because of the high dimensionality of Market Models, even those with a small number of stochastic drivers, is how can callable products be valued using Monte Carlo simulation?In this paper we consider the Longstaff-Schwartz algorithm, an effective algorithm developed to answer the second of these questions, and in so doing we shed light on the first of these questions. We show that the success of the Longstaff-Schwartz algorithm for high-dimensional models demonstrates that, in a way we make precise, low-dimensional models are sufficient, but that in another sense the higher dimensionality still plays a part.Using the insight gained from this analysis we go on to develop models which have these desirable properties - high dimensionality and accurate calibration properties on the one hand, but the ability to collapse the models onto lower-dimensional 'core' models for the purposes of valuing callable derivatives. The core models that we develop are Markovian and can thus be implemented efficiently using lattice methods, avoiding the need for more costly Monte Carlo simulation.
Book Synopsis A Comparison of Single Factor Markov-functional and Multi Factor Market Models by : Raoul Pietersz
Download or read book A Comparison of Single Factor Markov-functional and Multi Factor Market Models written by Raoul Pietersz and published by . This book was released on 2005 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Markov Functional Modeling of Equity, Commodity and Other Assets by : Christian P. Fries
Download or read book Markov Functional Modeling of Equity, Commodity and Other Assets written by Christian P. Fries and published by . This book was released on 2006 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this short note we show how to setup a one dimensional single asset model, e.g. equity model, which calibrates to a full (two dimensional) implied volatility surface. We show that the efficient calibration procedure used in LIBOR Markov functional models may be applied here too. In a addition to the calibration to a full volatility surface the model allows the calibration of the joint asset-interest rate movement (i.e. local interest rates) and forward volatility. The latter allows the calibration of compound or Bermudan options.The Markov functional modeling approach consists of a Markovian driver process x and a mapping functional representing the asset states S(t) as a function of x(t). It was originally developed in the context of interest rate models, see [Hunt Kennedy Pelsser 2000]. Our approach however is similar to the setup of the hybrid Markov functional model in spot measure, as considered in [Fries Rott 2004].For equity models it is common to use a deterministic Numeacute;raire, e.g. the bank account with deterministic interest rates. In our approach we will choose the asset itself as Numeacute;raire. This is a subtle, but crucial difference to other approaches considering Markov functional modeling. Choosing the asset itself as Numeacute;raire will allow for a very efficient numerically calibration procedure. As a consequence interest rates have to be allowed to be stochastic, namely as a functional of x too. The Black-Scholes model with deterministic interest rates is a special case of such a Markov functional model.The most general form of this modeling approach will allow for a simultaneous calibration to a full two dimensional volatility smile, a prescribed joint movement of interest rates and a given forward volatility structure.
Book Synopsis Mathematical Finance by : Christian Fries
Download or read book Mathematical Finance written by Christian Fries and published by John Wiley & Sons. This book was released on 2007-10-19 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: A balanced introduction to the theoretical foundations and real-world applications of mathematical finance The ever-growing use of derivative products makes it essential for financial industry practitioners to have a solid understanding of derivative pricing. To cope with the growing complexity, narrowing margins, and shortening life-cycle of the individual derivative product, an efficient, yet modular, implementation of the pricing algorithms is necessary. Mathematical Finance is the first book to harmonize the theory, modeling, and implementation of today's most prevalent pricing models under one convenient cover. Building a bridge from academia to practice, this self-contained text applies theoretical concepts to real-world examples and introduces state-of-the-art, object-oriented programming techniques that equip the reader with the conceptual and illustrative tools needed to understand and develop successful derivative pricing models. Utilizing almost twenty years of academic and industry experience, the author discusses the mathematical concepts that are the foundation of commonly used derivative pricing models, and insightful Motivation and Interpretation sections for each concept are presented to further illustrate the relationship between theory and practice. In-depth coverage of the common characteristics found amongst successful pricing models are provided in addition to key techniques and tips for the construction of these models. The opportunity to interactively explore the book's principal ideas and methodologies is made possible via a related Web site that features interactive Java experiments and exercises. While a high standard of mathematical precision is retained, Mathematical Finance emphasizes practical motivations, interpretations, and results and is an excellent textbook for students in mathematical finance, computational finance, and derivative pricing courses at the upper undergraduate or beginning graduate level. It also serves as a valuable reference for professionals in the banking, insurance, and asset management industries.
Book Synopsis A One-Factor Lognormal Markovian Interest Rate Model by : Anlong Li
Download or read book A One-Factor Lognormal Markovian Interest Rate Model written by Anlong Li and published by . This book was released on 2006 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a parsimonious Markovian interest rate model where the logarithm of the interest rate process is a scaled and shifted Ornstein-Uhlenbeck process. The model has many desirable properties such as lognormal distributed rates, mean reversion, and time-varying parameters. The corresponding discrete (lattice) approximation reduces to the discretization of the Ornstein-Uhlenbeck process, as we demonstrate by a simple and efficient trinomial lattice. In calibrating the model to the initial yield curve (or, equivalently, the term structure of zero-coupon bonds), we need only solve a linear equation instead of a nonlinear one as in current practice. This saves a considerable amount of computation time, especially in calibrating the model to interest rate options where calibrating to the yield curve is repeated many times over. The paper also discusses the merits of Monte-Carlo simulation of paths from the calibrated lattice.
Book Synopsis Interest Rate Modeling by : Lixin Wu
Download or read book Interest Rate Modeling written by Lixin Wu and published by CRC Press. This book was released on 2019-03-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing many results that are new, or which exist only in recent research articles, Interest Rate Modeling: Theory and Practice, 2nd Edition portrays the theory of interest rate modeling as a three-dimensional object of finance, mathematics, and computation. It introduces all models with financial-economical justifications, develops options along the martingale approach, and handles option evaluations with precise numerical methods. Features Presents a complete cycle of model construction and applications, showing readers how to build and use models Provides a systematic treatment of intriguing industrial issues, such as volatility and correlation adjustments Contains exercise sets and a number of examples, with many based on real market data Includes comments on cutting-edge research, such as volatility-smile, positive interest-rate models, and convexity adjustment New to the 2nd edition: volatility smile modeling; a new paradigm for inflation derivatives modeling; an extended market model for credit derivatives; a dual-curved model for the post-crisis interest-rate derivatives markets; and an elegant framework for the xVA.
Book Synopsis The General Hull-White Model and Super Calibration by : John C. Hull
Download or read book The General Hull-White Model and Super Calibration written by John C. Hull and published by . This book was released on 2008 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Term structure models are widely used to price interest-rate derivatives such as swaps and bonds with embedded options. This paper describes how a general one-factor model of the short-rate can be implemented as a recombining trinomial tree and calibrated to market prices of actively traded instruments such as caps and swap options. The general model encompasses most popular one-factor Markov models as special cases. The implementation and the calibration procedures are sufficiently general that they can select the functional form of the model that best fits the market prices. This allows the model to fit the prices of in- and out-ofthe-money options when there is a volatility skew. It also allows the model to work well very low interest-rate economies such as Japan where other models often fail.
