Efficient Simulation Of Generalized Sabr And Stochastic Local Volatility Models Based On Markov Chain Approximations

Download Efficient Simulation Of Generalized Sabr And Stochastic Local Volatility Models Based On Markov Chain Approximations full books in PDF, epub, and Kindle. Read online Efficient Simulation Of Generalized Sabr And Stochastic Local Volatility Models Based On Markov Chain Approximations ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!

Efficient Simulation of Generalized SABR and Stochastic Local Volatility Models Based on Markov Chain Approximations

Author : Zhenyu Cui
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Efficient Simulation of Generalized SABR and Stochastic Local Volatility Models Based on Markov Chain Approximations by : Zhenyu Cui

Download or read book Efficient Simulation of Generalized SABR and Stochastic Local Volatility Models Based on Markov Chain Approximations written by Zhenyu Cui and published by . This book was released on 2020 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a novel Monte Carlo simulation method for two-dimensional stochastic differential equation (SDE) systems based on approximation through continuous-time Markov chains (CTMCs). Specifically, we propose an efficient simulation framework for asset prices under general stochastic local volatility (SLV) models arising in finance, which includes the Heston and the stochastic alpha beta rho (SABR) models as special cases. Our simulation algorithm is constructed based on approximating the latent stochastic variance process by a CTMC. Compared with time-discretization schemes, our method exhibits several advantages, including flexible boundary condition treatment, weak continuity conditions imposed on coefficients, and a second order convergence rate in the spatial grids of the approximating CTMC under suitable regularity conditions. Replacing the stochastic variance process with a discrete-state approximation greatly simplifies the direct sampling of the integrated variance, thus enabling a highly efficient simulation scheme. Extensive numerical examples illustrate the accuracy and efficiency of our estimator, which outperforms both biased and unbiased simulation estimators in the literature in terms of root mean squared error (RMSE) and computational time. This paper is focused primarily on the simulation of SDEs which arise in finance, but this new simulation approach has potential for applications in other contextual areas in operations research, such as queuing theory.

Markov Chain Monte Carlo Methods for Generalized Stochastic Volatility Models

Author : Siddhartha Chib
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

DOWNLOAD NOW!

Book Synopsis Markov Chain Monte Carlo Methods for Generalized Stochastic Volatility Models by : Siddhartha Chib

Download or read book Markov Chain Monte Carlo Methods for Generalized Stochastic Volatility Models written by Siddhartha Chib and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy-tailed student-t distributions (with unknown degrees of freedom) and covariate effects in the observation and volatility equations and a jump component in the observation equation. By building on the work of Kim, Shephard and Chib (1998), we develop efficient Markov chain Monte Carlo algorithms for estimating these models. The paper also discusses how the likelihood function of these models can be computed by appropriate particle filter methods. Computation of the marginal likelihood by the method of Chib (1995) is also considered. The methodology is extensively tested and validated on simulated data and then applied in detail to daily returns data on the S&P 500 index where several stochastic volatility models are formally compared under various priors on the parameters.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

DOWNLOAD NOW!

Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

A General Valuation Framework for SABR and Stochastic Local Volatility Models

Author : Zhenyu Cui
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (13 download)

DOWNLOAD NOW!

Book Synopsis A General Valuation Framework for SABR and Stochastic Local Volatility Models by : Zhenyu Cui

Download or read book A General Valuation Framework for SABR and Stochastic Local Volatility Models written by Zhenyu Cui and published by . This book was released on 2019 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Rethinking ICT Adoption Theories in the Developing World

Author : Emmanuel Eilu
Publisher : Springer Nature
ISBN 13 : 3031578805
Total Pages : 288 pages
Book Rating : 4.0/5 (315 download)

DOWNLOAD NOW!

Book Synopsis Rethinking ICT Adoption Theories in the Developing World by : Emmanuel Eilu

Download or read book Rethinking ICT Adoption Theories in the Developing World written by Emmanuel Eilu and published by Springer Nature. This book was released on with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Markov Chain Monte Carlo

Author : Dani Gamerman
Publisher : CRC Press
ISBN 13 : 148229642X
Total Pages : 342 pages
Book Rating : 4.4/5 (822 download)

DOWNLOAD NOW!

Book Synopsis Markov Chain Monte Carlo by : Dani Gamerman

Download or read book Markov Chain Monte Carlo written by Dani Gamerman and published by CRC Press. This book was released on 2006-05-10 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there have been few theoretical contributions on the Markov Chain Monte Carlo (MCMC) methods in the past decade, current understanding and application of MCMC to the solution of inference problems has increased by leaps and bounds. Incorporating changes in theory and highlighting new applications, Markov Chain Monte Carlo: Stochastic Simul

Markov Chains

Author : Pierre Bremaud
Publisher : Springer Science & Business Media
ISBN 13 : 1475731248
Total Pages : 456 pages
Book Rating : 4.4/5 (757 download)

DOWNLOAD NOW!

Book Synopsis Markov Chains by : Pierre Bremaud

Download or read book Markov Chains written by Pierre Bremaud and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.

Efficient Simulation of the Heston Stochastic Volatility Model

Author : Leif B. G. Andersen
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (129 download)

DOWNLOAD NOW!

Book Synopsis Efficient Simulation of the Heston Stochastic Volatility Model by : Leif B. G. Andersen

Download or read book Efficient Simulation of the Heston Stochastic Volatility Model written by Leif B. G. Andersen and published by . This book was released on 2007 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility models are increasingly important in practical derivatives pricing applications, yet relatively little work has been undertaken in the development of practical Monte Carlo simulation methods for this class of models. This paper considers several new algorithms for time-discretization and Monte Carlo simulation of Heston-type stochastic volatility models. The algorithms are based on a careful analysis of the properties of affine stochastic volatility diffusions, and are straightforward and quick to implement and execute. Tests on realistic model parameterizations reveal that the computational efficiency and robustness of the simulation schemes proposed in the paper compare very favorably to existing methods.

Modelling and Simulation of Stochastic Volatility in Finance

Author : Christian Kahl
Publisher : Universal-Publishers
ISBN 13 : 1581123833
Total Pages : 219 pages
Book Rating : 4.5/5 (811 download)

DOWNLOAD NOW!

Book Synopsis Modelling and Simulation of Stochastic Volatility in Finance by : Christian Kahl

Download or read book Modelling and Simulation of Stochastic Volatility in Finance written by Christian Kahl and published by Universal-Publishers. This book was released on 2008 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.

Markov Chain Monte Carlo

Author : Dani Gamerman
Publisher : CRC Press
ISBN 13 : 9780412818202
Total Pages : 264 pages
Book Rating : 4.8/5 (182 download)

DOWNLOAD NOW!

Book Synopsis Markov Chain Monte Carlo by : Dani Gamerman

Download or read book Markov Chain Monte Carlo written by Dani Gamerman and published by CRC Press. This book was released on 1997-10-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between research and application, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference provides a concise, and integrated account of Markov chain Monte Carlo (MCMC) for performing Bayesian inference. This volume, which was developed from a short course taught by the author at a meeting of Brazilian statisticians and probabilists, retains the didactic character of the original course text. The self-contained text units make MCMC accessible to scientists in other disciplines as well as statisticians. It describes each component of the theory in detail and outlines related software, which is of particular benefit to applied scientists.

Stochastic Volatility and Realized Stochastic Volatility Models

Author : Makoto Takahashi
Publisher : Springer Nature
ISBN 13 : 981990935X
Total Pages : 120 pages
Book Rating : 4.8/5 (199 download)

DOWNLOAD NOW!

Book Synopsis Stochastic Volatility and Realized Stochastic Volatility Models by : Makoto Takahashi

Download or read book Stochastic Volatility and Realized Stochastic Volatility Models written by Makoto Takahashi and published by Springer Nature. This book was released on 2023-04-18 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.

Markov-functional and Stochastic Volatility Modelling

Author : Duy Pham
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (857 download)

DOWNLOAD NOW!

Book Synopsis Markov-functional and Stochastic Volatility Modelling by : Duy Pham

Download or read book Markov-functional and Stochastic Volatility Modelling written by Duy Pham and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study two practical problems in applied mathematical fi nance. The first topic discusses the issue of pricing and hedging Bermudan swaptions within a one factor Markov-functional model. We focus on the implications for hedging of the choice of instantaneous volatility for the one-dimensional driving Markov process of the model. We find that there is a strong evidence in favour of what we term \parametrization by time" as opposed to \parametrization by expiry". We further propose a new parametrization by time for the driving process which takes as inputs into the model the market correlations of relevant swap rates. We show that the new driving process enables a very effective vega-delta hedge with a much more stable gamma profile for the hedging portfolio compared with the existing ones. The second part of the thesis mainly addresses the topic of pricing European options within the popular stochastic volatility SABR model and its extension with mean reversion. We investigate some effcient approximations for these models to be used in real time. We first derive a probabilistic approximation for three different versions of the SABR model: Normal, Log-Normal and a displaced diffusion version for the general constant elasticity of variance case. Specifically, we focus on capturing the terminal distribution of the underlying process (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a variety of parameters which cover long dated options and highly stress market condition. This is a different feature from other current approaches which rely on the assumption of very small total volatility and usually fail for longer than 10 years maturity or large volatility of volatility. A similar study is done for the extension of the SABR model with mean reversion (SABR-MR). We first compare the SABR model with this extended model in terms of forward volatility to point out the fundamental difference in the dynamics of the two models. This is done through a numerical example of pricing forward start options. We then derive an effcient probabilistic approximation for the SABRMR model to price European options in a similar fashion to the one for the SABR model. The numerical results are shown to be still satisfactory for a wide range of market conditions.

Monte Carlo Methods in Finance

Author : Peter Jäckel
Publisher : John Wiley & Sons
ISBN 13 : 047149741X
Total Pages : 245 pages
Book Rating : 4.4/5 (714 download)

DOWNLOAD NOW!

Book Synopsis Monte Carlo Methods in Finance by : Peter Jäckel

Download or read book Monte Carlo Methods in Finance written by Peter Jäckel and published by John Wiley & Sons. This book was released on 2002-04-03 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: An invaluable resource for quantitative analysts who need to run models that assist in option pricing and risk management. This concise, practical hands on guide to Monte Carlo simulation introduces standard and advanced methods to the increasing complexity of derivatives portfolios. Ranging from pricing more complex derivatives, such as American and Asian options, to measuring Value at Risk, or modelling complex market dynamics, simulation is the only method general enough to capture the complexity and Monte Carlo simulation is the best pricing and risk management method available. The book is packed with numerous examples using real world data and is supplied with a CD to aid in the use of the examples.

A Weak Approximation with Malliavin Weights for Local Stochastic Volatility Model

Author : Toshihiro Yamada
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (13 download)

DOWNLOAD NOW!

Book Synopsis A Weak Approximation with Malliavin Weights for Local Stochastic Volatility Model by : Toshihiro Yamada

Download or read book A Weak Approximation with Malliavin Weights for Local Stochastic Volatility Model written by Toshihiro Yamada and published by . This book was released on 2017 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a new efficient and practical weak approximation for option price under local stochastic volatility model as marginal expectation of stochastic differential equation, using iterative asymptotic expansion with Malliavin weights. The explicit Malliavin weights for SABR model are shown. Numerical experiments confirm the validity of our discretization with a few time steps.

Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing

Author : Zhenyu Cui
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (13 download)

DOWNLOAD NOW!

Book Synopsis Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing by : Zhenyu Cui

Download or read book Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing written by Zhenyu Cui and published by . This book was released on 2019 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this chapter, we present recent developments in using the tools of continuous-time Markov chains for the valuation of European and path-dependent financial derivatives. We also survey results on a newly proposed regime switching approximation to stochastic volatility, and stochastic local volatility models. The presented framework is part of an exciting recent stream of literature on numerical option pricing, and offers a new perspective that combines the theory of diffusion processes, Markov chains, and Fourier techniques. It is also elegantly connected to partial differential equation (PDE) approaches.

Markov Chains and Stochastic Stability

Author : Sean Meyn
Publisher : Cambridge University Press
ISBN 13 : 1139477978
Total Pages : 595 pages
Book Rating : 4.1/5 (394 download)

DOWNLOAD NOW!

Book Synopsis Markov Chains and Stochastic Stability by : Sean Meyn

Download or read book Markov Chains and Stochastic Stability written by Sean Meyn and published by Cambridge University Press. This book was released on 2009-04-02 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meyn and Tweedie is back! The bible on Markov chains in general state spaces has been brought up to date to reflect developments in the field since 1996 - many of them sparked by publication of the first edition. The pursuit of more efficient simulation algorithms for complex Markovian models, or algorithms for computation of optimal policies for controlled Markov models, has opened new directions for research on Markov chains. As a result, new applications have emerged across a wide range of topics including optimisation, statistics, and economics. New commentary and an epilogue by Sean Meyn summarise recent developments and references have been fully updated. This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.

Mathematical Modeling and Methods of Option Pricing

Author : Lishang Jiang
Publisher : World Scientific
ISBN 13 : 9812563695
Total Pages : 344 pages
Book Rating : 4.8/5 (125 download)

DOWNLOAD NOW!

Book Synopsis Mathematical Modeling and Methods of Option Pricing by : Lishang Jiang

Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.