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Pricing Continuously Monitored Barrier Options Under The Sabr Model
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Book Synopsis Pricing Continuously Monitored Barrier Options Under the Sabr Model by : Nian Yang
Download or read book Pricing Continuously Monitored Barrier Options Under the Sabr Model written by Nian Yang and published by . This book was released on 2019 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stochastic alpha beta rho (SABR) model introduced by Hagan et al. (2002) is widely used in both fixed income and the foreign exchange (FX) markets. Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets. In this paper, we develop closed-form formulas to approximate various types of barrier option prices (down-and-out/in, up-and-out/in) under the SABR model. We first derive an approximate formula for the survival density. The barrier option price is the one-dimensional integral of its payoff function and the survival density, which can be easily implemented and quickly evaluated. The approximation error of the survival density is also analyzed. To the best of our knowledge, it is the first time that analytical (approximate) formulas for the survival density and the barrier option prices for the SABR model are derived. Numerical experiments demonstrate the validity and efficiency of these formulas.
Book Synopsis A Semi-Group Expansion for Pricing Barrier Options by : Takashi Kato
Download or read book A Semi-Group Expansion for Pricing Barrier Options written by Takashi Kato and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing barrier option in the log-normal SABR stochastic volatility model.
Book Synopsis Pricing Discretely Monitored Barrier Options by a Markov Chain by : Jin-Chuan Duan
Download or read book Pricing Discretely Monitored Barrier Options by a Markov Chain written by Jin-Chuan Duan and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The method here to price discretely monitored barrier options in both constant and time-varying volatility valuation frameworks uses a time-homogeneous Markov chain to approximate the underlying asset price process. It provides a natural framework for this pricing process because the discrete time step of the Markov chain can be easily matched with the monitoring frequency of the barrier. The underlying asset price can also be partitioned so as to place the barrier suitably. The method can efficiently handle difficult cases where the barrier is close to the initial asset price. Examples include both knock-in and knock-out barrier options. Different types of barriers such as single, double, and moving barriers are also analyzed.
Book Synopsis Large Deviations and Asymptotic Methods in Finance by : Peter K. Friz
Download or read book Large Deviations and Asymptotic Methods in Finance written by Peter K. Friz and published by Springer. This book was released on 2015-06-16 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
Book Synopsis The Time-Dependent FX-SABR Model by : Anthonie van der Stoep
Download or read book The Time-Dependent FX-SABR Model written by Anthonie van der Stoep and published by . This book was released on 2015 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a framework for efficient calibration of the time-dependent SABR model in an FX context. In a similar fashion as in Piterbarg (2005) we derive effective parameters, which yield an accurate and efficient calibration. On top of the calibrated FX-SABR model we add a non-parametric local volatility component, which naturally compensates for possible calibration errors. By means of Monte Carlo pricing experiments we show that the time-dependent FX-SABR model enables an accurate and consistent pricing of barrier options and outperforms the constant-parameter SABR model and the traditional Local Volatility model. We also consider the role of the local volatility component in pricing barrier options.
Book Synopsis Barrier Options on Spot Libor Rates Under Multi-Factor Gaussian HJM Models by : João Pedro Vidal Nunes
Download or read book Barrier Options on Spot Libor Rates Under Multi-Factor Gaussian HJM Models written by João Pedro Vidal Nunes and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive approximate analytical pricing formulas for interest rate caps and floors with continuously monitored barriers in a multi-factor Gaussian HJM framework. The closed-form valuation equations are subject to a Radon-Nikodym approximation, which is similar to the proportionality assumption used by El Karoui and Rochet (1989) and to the rank 1 approximation suggested by Brace and Musiela (1994).Monte Carlo simulation shows that the resulting analytical approximations are accurate and much faster than existing numerical and quasi-analytical pricing methods. Moreover, we provide error bounds for our solution, an innovation relative to the previous literature. These bounds provide a confidence interval for the true barrier option price, which in turn is an indicator of the precision of the proposed analytical pricing solutions.
Book Synopsis Smile Pricing Explained by : P. Austing
Download or read book Smile Pricing Explained written by P. Austing and published by Springer. This book was released on 2014-08-29 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smile Pricing Explained provides a clear and thorough explanation of the concepts of smile modelling that are at the forefront of modern derivatives pricing. The key models used in practice are covered, together with numerical techniques and calibration.
Book Synopsis Option Pricing and Estimation of Financial Models with R by : Stefano M. Iacus
Download or read book Option Pricing and Estimation of Financial Models with R written by Stefano M. Iacus and published by John Wiley & Sons. This book was released on 2011-02-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
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 2019-04-23 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 Pricing of Discretely Monitored Barrier Options by :
Download or read book Pricing of Discretely Monitored Barrier Options written by and published by . This book was released on 2014 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis FX Options and Structured Products by : Uwe Wystup
Download or read book FX Options and Structured Products written by Uwe Wystup and published by John Wiley & Sons. This book was released on 2017-06-30 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Guidance to Excelling in the FX Market Once you have a textbook understanding of money market and foreign exchange products, turn to FX Options and Structured Products, Second Edition, for the beyond-vanilla options strategies and traded deals proven superior in today’s post-credit crisis trading environment. With the thoroughness and balance of theory and practice only Uwe Wystup can deliver, this fully revised edition offers authoritative solutions for the real world in an easy-to-access format. See how specific products actually work through detailed case studies featuring clear examples of FX options, common structures and custom solutions. This complete resource is both a wellspring of ideas and a hands-on guide to structuring and executing your own strategies. Distinguish yourself with a valued skillset by: Working through practical and thought-provoking challenges in more than six dozen exercises, all with complete solutions in a companion volume Gaining a working knowledge of the latest, most popular products, including accumulators, kikos, target forwards and more Getting close to the everyday realities of the FX derivatives market through new, illuminating case studies for corporates, municipalities and private banking FX Options and Structured Products, Second Edition is your go-to road map to the exotic options in FX derivatives.
Book Synopsis Financial Modelling by : Joerg Kienitz
Download or read book Financial Modelling written by Joerg Kienitz and published by John Wiley & Sons. This book was released on 2013-02-18 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial modelling Theory, Implementation and Practice with MATLAB Source Jörg Kienitz and Daniel Wetterau Financial Modelling - Theory, Implementation and Practice with MATLAB Source is a unique combination of quantitative techniques, the application to financial problems and programming using Matlab. The book enables the reader to model, design and implement a wide range of financial models for derivatives pricing and asset allocation, providing practitioners with complete financial modelling workflow, from model choice, deriving prices and Greeks using (semi-) analytic and simulation techniques, and calibration even for exotic options. The book is split into three parts. The first part considers financial markets in general and looks at the complex models needed to handle observed structures, reviewing models based on diffusions including stochastic-local volatility models and (pure) jump processes. It shows the possible risk-neutral densities, implied volatility surfaces, option pricing and typical paths for a variety of models including SABR, Heston, Bates, Bates-Hull-White, Displaced-Heston, or stochastic volatility versions of Variance Gamma, respectively Normal Inverse Gaussian models and finally, multi-dimensional models. The stochastic-local-volatility Libor market model with time-dependent parameters is considered and as an application how to price and risk-manage CMS spread products is demonstrated. The second part of the book deals with numerical methods which enables the reader to use the models of the first part for pricing and risk management, covering methods based on direct integration and Fourier transforms, and detailing the implementation of the COS, CONV, Carr-Madan method or Fourier-Space-Time Stepping. This is applied to pricing of European, Bermudan and exotic options as well as the calculation of the Greeks. The Monte Carlo simulation technique is outlined and bridge sampling is discussed in a Gaussian setting and for Lévy processes. Computation of Greeks is covered using likelihood ratio methods and adjoint techniques. A chapter on state-of-the-art optimization algorithms rounds up the toolkit for applying advanced mathematical models to financial problems and the last chapter in this section of the book also serves as an introduction to model risk. The third part is devoted to the usage of Matlab, introducing the software package by describing the basic functions applied for financial engineering. The programming is approached from an object-oriented perspective with examples to propose a framework for calibration, hedging and the adjoint method for calculating Greeks in a Libor market model. Source code used for producing the results and analysing the models is provided on the author's dedicated website, http://www.mathworks.de/matlabcentral/fileexchange/authors/246981.
Book Synopsis Approximate and PDE Solution to the Boundary Free SABR Model - Applications to Pricing and Calibration by : Joerg Kienitz
Download or read book Approximate and PDE Solution to the Boundary Free SABR Model - Applications to Pricing and Calibration written by Joerg Kienitz and published by . This book was released on 2015 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considering the current interest rate environment it has become necessary to extend option pricing models for 0 and negative strikes. We consider the recently proposed free boundary SABR model, Antonov A., Konikov, M., and Spector, M. (2015). In their paper the authors provide a pricing formula for European Call options based on numerical integration and Markovian projection. Since it is necessary for practitioners to calibrate the model to market data fast approximation methods together with benchmark methods for their performance are essential. In this note we consider the PDE solution for pricing European Call options as well as two approximation formulas for the Bachelier, aka Normal volatility, produced by this model. The latter numbers can then be plugged into the Bachelier pricing formula to get the corresponding option prices.We have to stress two facts. First, the PDE method can be seen as a benchmark for the approximate solutions and, second, the approximation formulas can serve for calibration purposes, where fast calculation methods are essential, especially, if one wishes to calibrate to implied Bachelier volatilities. In the approach proposed by Antonov A., Konikov, M., and Spector, M. (2015) the implied volatilities have to be inferred from option prices.Finally, we stress the fact that the PDE or approximate solutions can be used to effciently apply a mixing approach to control the shape of the surface, especially the wings.
Book Synopsis Complete Analytical Solution of the SABR Model for Fixed-Income Option Pricing and Value-at-Risk Problems - A Probability Density Function Approach by : Alexander Izmailov
Download or read book Complete Analytical Solution of the SABR Model for Fixed-Income Option Pricing and Value-at-Risk Problems - A Probability Density Function Approach written by Alexander Izmailov and published by . This book was released on 2016 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first ever explicit f ...
Book Synopsis Exotic Options and Hybrids by : Mohamed Bouzoubaa
Download or read book Exotic Options and Hybrids written by Mohamed Bouzoubaa and published by John Wiley & Sons. This book was released on 2010-05-17 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent financial crisis brought to light many of the misunderstandings and misuses of exotic derivatives. With market participants on both the buy and sell-side having been found guilty of not understanding the products they were dealing with, never before has there been a greater need for clarification and explanation. Exotic Options and Hybrids is a practical guide to structuring, pricing and hedging complex exotic options and hybrid derivatives that will serve readers through the recent crisis, the road to recovery, the next bull market and beyond. Written by experienced practitioners, it focuses on the three main parts of a derivative’s life: the structuring of a product, its pricing and its hedging. Divided into four parts, the book covers a multitude of structures, encompassing many of the most up-to-date and promising products from exotic equity derivatives and structured notes to hybrid derivatives and dynamic strategies. Based on a realistic setting from the heart of the business, inside a derivatives operation, the practical and intuitive discussions of these aspects make these exotic concepts truly accessible. Adoptions of real trades are examined in detail, and all of the numerous examples are carefully selected so as to highlight interesting and significant aspects of the business. The introduction of payoff structures is accompanied by scenario analysis, diagrams and lifelike sample term sheets. Readers learn how to spot where the risks lie to pave the way for sound valuation and hedging of such products. There are also questions and accompanying discussions dispersed in the text, each exploited to illustrate one or more concepts from the context in which they are set. The applications, the strengths and the limitations of various models are highlighted, in relevance to the products and their risks, rather than the model implementations. Models are de-mystified in separately dedicated sections, but their implications are alluded to throughout the book in an intuitive and non-mathematical manner. By discussing exotic options and hybrids in a practical, non-mathematical and highly intuitive setting, this book will blast through the misunderstanding of exotic derivatives, enabling practitioners to fully understand and correctly structure, price and hedge theses products effectively, and stand strong as the only book in its class to make these “exotic” concepts truly accessible.
Book Synopsis Pricing Early-Exercise and Discrete Barrier Options by Shannon Wavelet Expansions by : Stefanus Maree
Download or read book Pricing Early-Exercise and Discrete Barrier Options by Shannon Wavelet Expansions written by Stefanus Maree and published by . This book was released on 2016 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a pricing method based on Shannon wavelet expansions for early-exercise and discretely-monitored barrier options under exponential Lévy asset dynamics. Shannon wavelets are smooth, and thus approximate the densities that occur in finance well, resulting in exponential convergence. Application of the Fast Fourier Transform yields an efficient implementation and since wavelet are local approximations, the domain boundary errors can be naturally resolved, which is the main improvement over existing methods.
Book Synopsis Full-fledged SABR Through Markov Chains by : Zhenyu Cui
Download or read book Full-fledged SABR Through Markov Chains written by Zhenyu Cui and published by . This book was released on 2019 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a general purpose technique for the efficient and accurate valuation of options in the shifted Stochastic Alpha Beta Rho (shifted-SABR) model which includes SABR as a special case. The method is based on a novel double-layer continuous-time Markov chain (CTMC) from which closed-form matrix expressions for European options are derived. We also propose a recursive risk-neutral valuation technique for pricing discretely monitored path-dependent options, and use it to price Bermudan and barrier options. In addition, we provide single Laplace transform formula for discretely monitored arithmetic Asian options. Numerical experiments confirm the accuracy and efficiency of the proposed method, which is suitable for practical use.
