Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Analytical Approximation Of The Transition Density In A Local Volatility Model
Download Analytical Approximation Of The Transition Density In A Local Volatility Model full books in PDF, epub, and Kindle. Read online Analytical Approximation Of The Transition Density In A Local Volatility Model ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Book Synopsis Analytical Approximation of the Transition Density in a Local Volatility Model by : Andrea Pascucci
Download or read book Analytical Approximation of the Transition Density in a Local Volatility Model written by Andrea Pascucci and published by . This book was released on 2016 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a simplified approach to the analytical approximation of the transition density related to a general local volatility model. The methodology is sufficiently flexible to be extended to time-dependent coefficients, multi-dimensional stochastic volatility models, degenerate parabolic PDEs related to Asian options and also to include jumps.
Book Synopsis Adjoint Expansions in Local Lévy Models by : Stefano Pagliarani
Download or read book Adjoint Expansions in Local Lévy Models written by Stefano Pagliarani and published by . This book was released on 2016 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a novel method for the analytical approximation in local volatility models with Lévy jumps. The main result is an expansion of the characteristic function in a local Lévy model, which is worked out in the Fourier space by considering the adjoint formulation of the pricing problem. Combined with standard Fourier methods, our result provides efficient and accurate pricing formulae. In the case of Gaussian jumps, we also derive an explicit approximation of the transition density of the underlying process by a heat kernel expansion: the approximation is obtained in two ways, using PIDE techniques and working in the Fourier space. Numerical tests confirm the effectiveness of the method.
Book Synopsis Applied Modeling Techniques and Data Analysis 2 by : Yiannis Dimotikalis
Download or read book Applied Modeling Techniques and Data Analysis 2 written by Yiannis Dimotikalis and published by John Wiley & Sons. This book was released on 2021-04-13 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: BIG DATA, ARTIFICIAL INTELLIGENCE AND DATA ANALYSIS SET Coordinated by Jacques Janssen Data analysis is a scientific field that continues to grow enormously, most notably over the last few decades, following rapid growth within the tech industry, as well as the wide applicability of computational techniques alongside new advances in analytic tools. Modeling enables data analysts to identify relationships, make predictions, and to understand, interpret and visualize the extracted information more strategically. This book includes the most recent advances on this topic, meeting increasing demand from wide circles of the scientific community. Applied Modeling Techniques and Data Analysis 2 is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians, working on the front end of data analysis and modeling applications. The chapters cover a cross section of current concerns and research interests in the above scientific areas. The collected material is divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with appropriate applications.
Book Synopsis Implied Volatility from Local Volatility by : Tai-Ho Wang
Download or read book Implied Volatility from Local Volatility written by Tai-Ho Wang and published by . This book was released on 2015 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming local volatility, we derive an exact Brownian bridge representation for the transition density; an exact expression for the transition density in terms of a path integral then follows. By Taylor-expanding around a certain path, we obtain a generalization of the heat kernel expansion of the density which coincides with the classical one in the time-homogeneous case, but is more accurate and natural in the time inhomogeneous case. As a further application of our path integral representation, we obtain an improved most-likely-path approximation for implied volatility in terms of local volatility.
Book Synopsis Perturbation Methods in Credit Derivatives by : Colin Turfus
Download or read book Perturbation Methods in Credit Derivatives written by Colin Turfus and published by John Wiley & Sons. This book was released on 2021-03-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stress-test financial models and price credit instruments with confidence and efficiency using the perturbation approach taught in this expert volume Perturbation Methods in Credit Derivatives: Strategies for Efficient Risk Management offers an incisive examination of a new approach to pricing credit-contingent financial instruments. Author and experienced financial engineer Dr. Colin Turfus has created an approach that allows model validators to perform rapid benchmarking of risk and pricing models while making the most efficient use possible of computing resources. The book provides innumerable benefits to a wide range of quantitative financial experts attempting to comply with increasingly burdensome regulatory stress-testing requirements, including: Replacing time-consuming Monte Carlo simulations with faster, simpler pricing algorithms for front-office quants Allowing CVA quants to quantify the impact of counterparty risk, including wrong-way correlation risk, more efficiently Developing more efficient algorithms for generating stress scenarios for market risk quants Obtaining more intuitive analytic pricing formulae which offer a clearer intuition of the important relationships among market parameters, modelling assumptions and trade/portfolio characteristics for traders The methods comprehensively taught in Perturbation Methods in Credit Derivatives also apply to CVA/DVA calculations and contingent credit default swap pricing.
Book Synopsis Analytical Formulas for Local Volatility Model with Stochastic Rates by : Eric Benhamou
Download or read book Analytical Formulas for Local Volatility Model with Stochastic Rates written by Eric Benhamou and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents new approximation formulae of European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1275872 for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of stochastic dividends or stochastic convenience yields. We finally provide numerical results to illustrate the accuracy with real market data.
Book Synopsis Local Stochastic Volatility with Jumps by : Stefano Pagliarani
Download or read book Local Stochastic Volatility with Jumps written by Stefano Pagliarani and published by . This book was released on 2016 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.
Book Synopsis Fitting Local Volatility by : Andrey Itkin
Download or read book Fitting Local Volatility written by Andrey Itkin and published by . This book was released on 2020 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On a New Parametrization Class of Solvable Diffusion Models and Transition Probability Kernels by : Sebastian Tudor
Download or read book On a New Parametrization Class of Solvable Diffusion Models and Transition Probability Kernels written by Sebastian Tudor and published by . This book was released on 2018 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present in this paper a novel parametrization class of analytically tractable local volatility diffusion models used to price and hedge financial derivatives. A complete theoretical framework for computing the local volatility and the transition probability density is provided along with efficient model calibration for vanilla option prices, and reliable extrapolation procedures for producing the volatility surface. Our approach is based on the spectral analysis of the pricing operator in the time invariant case, along with some specific properties of the class that we propose. In order to show the advantages of our model, numerical examples with market data are analyzed. Finally, some extensions of our parametrization class are discussed in the conclusions.
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 A Threshold Model for Local Volatility: Evidence of Leverage and Mean Reversion Effects on Historical Data by : Antoine Lejay
Download or read book A Threshold Model for Local Volatility: Evidence of Leverage and Mean Reversion Effects on Historical Data written by Antoine Lejay and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial markets, low prices are generally associated with high volatilities and vice-versa, this well known stylized fact usually being referred to as leverage effect. We propose a local volatility model, given by a stochastic differential equation with piecewise constant coefficients, which accounts of leverage and mean-reversion effects in the dynamics of the prices. This model exhibits a regime switch in the dynamics accordingly to a certain threshold. It can be seen as a continuous time version of the Self-Exciting Threshold Autoregressive (SETAR) model. We propose an estimation procedure for the volatility and drift coefficients as well as for the threshold level. Tests are performed on the daily prices of 21 assets. They show empirical evidence for leverage and mean-reversion effects, consistent with the results in the literature.
Book Synopsis Quantitative Analysis in Financial Markets by : Marco Avellaneda
Download or read book Quantitative Analysis in Financial Markets written by Marco Avellaneda and published by World Scientific. This book was released on 1999 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lectures presented at the Courant Institute's Mathematical Finance Seminar.
Book Synopsis Estimation of Volatilities Under a Merton's Jump-diffusion Model and an Uncertain Volatility Model by : Changhong He
Download or read book Estimation of Volatilities Under a Merton's Jump-diffusion Model and an Uncertain Volatility Model written by Changhong He and published by . This book was released on 2005 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Innovation for the Local Volatility Surface by : Hyuncheul Lim
Download or read book An Innovation for the Local Volatility Surface written by Hyuncheul Lim and published by . This book was released on 2020 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a new innovative method for the calibration of local volatility under Dupire's model. First, our proposed method approximates the Arrow-Debreu(AD) prices on the finite difference nodes as a low-dimensional function based on implied distribution estimation. This makes the function values from the continuous state space and the point values of the finite difference method coincide at the nodes. As a result, the instability caused by the discretization is structurally eliminated. Second, we derive three different Kolmogorov forward equations that can be used to generate the local volatility surface, and for Dupire's PDE, we can change the problem of finding the local volatility to the sole calculation of a simple linear equation. This gives us the remarkable results that are very robust, include no significant reconstruction error, and do not have any of the calculation time issues that the existing methods have. We show our researching process in detail, including the analysis of the existing articles, a detailed description of the algorithm used, and test results with figures.
Book Synopsis Stochastic Volatility Modeling by : Lorenzo Bergomi
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.
Book Synopsis Inference in Hidden Markov Models by : Olivier Cappé
Download or read book Inference in Hidden Markov Models written by Olivier Cappé and published by Springer Science & Business Media. This book was released on 2006-04-12 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of inference for hidden Markov models, including both algorithms and statistical theory. Topics range from filtering and smoothing of the hidden Markov chain to parameter estimation, Bayesian methods and estimation of the number of states. In a unified way the book covers both models with finite state spaces and models with continuous state spaces (also called state-space models) requiring approximate simulation-based algorithms that are also described in detail. Many examples illustrate the algorithms and theory. This book builds on recent developments to present a self-contained view.
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
