Download or read book Efficient Almost Exact Simulation of the Heston Stochastic Volatility Model written by Alexander van Haastrecht and published by . This book was released on 2011 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: We deal with several efficient discretization methods for the simulation of the Heston stochastic volatility model. The resulting schemes can be used to calculate all kind of options and corresponding sensitivities, in particular the exotic options that cannot be valued with closed-form solutions. We focus on to the (computational) efficiency of the simulation schemes: though the Broadie and Kaya (2006) paper provided an exact simulation method for the Heston dynamics, we argue why its practical use might be limited. Instead we consider efficient approximations of the exact scheme, which try to exploit certain distributional features of the underlying variance process. The resulting methods are fast, highly accurate and easy to implement. We conclude by numerically comparing our new schemes to the exact scheme of Broadie and Kaya, the almost exact scheme of Smith, the Kahl-Jackel scheme, the Full Truncation scheme of Lord et al. and the Quadratic Exponential scheme of 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.

Download or read book The Heston Stochastic Local Volatility Model written by Anthonie van der Stoep and published by . This book was released on 2018 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a non-parametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire (1994) and Derman & Kani (1998). In particular, the additional local volatility component acts as a "compensator" that bridges the mismatch between the non-perfectly calibrated Heston model and the market quotes for European-type options. By means of numerical experiments we show that our scheme enables a consistent and fast pricing of products that are sensitive to the forward volatility skew. Detailed error analysis is also provided.

Download or read book Analytical Solvability and Exact Simulation of Stochastic Volatility Models with Jumps written by Pingping Jiang and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We perform a thorough investigation on the analytical solvability of general stochastic volatility (SV) models with Levy jumps and propose a unified, accurate, and efficient almost exact simulation method to price various financial derivatives. Our theoretical results lay a foundation for a range of valuation, calibration, and econometric problems. Our almost exact simulation method is applicable to a broad class of models and enables effective pricing of path-dependent financial derivatives, whereas the traditional exact simulation method is always tailor-made for some specific models and is generally time-consuming, which limits its use in the case of path-dependent financial derivatives. More specifically, by combining a decomposition technique with a change of measure approach, we first develop a simple probabilistic method to derive a unified formula for the conditional characteristic function of the log-asset price under general SV models with Levy jumps and show under which conditions this new formula admits a closed-form expression. The conditional and unconditional joint characteristic functions of the log-asset price and the integrated variance can be easily obtained as byproducts. Second, we take advantage of our main theoretical result, the Hilbert transform method, the interpolation technique, and the dimension reduction technique to construct unified and efficient almost exact simulation schemes. Finally, we apply our almost exact simulation method to price European options, discretely monitored weighted variance swaps, and discretely monitored variance options under a wide variety of SV models with Levy jumps. Extensive numerical examples demonstrate the high level of accuracy and efficiency of our almost exact simulation method in terms of bias, root-mean-squared error (RMS error), and CPU time.

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.

Download or read book Exact Simulation of the Wishart Stochastic Volatility Model written by Marco Huerner and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with the simulation of the Wishart stochastic volatility model (WSVM) which is a matrix generalization of the famous Heston model. Lately, an exact sampling scheme has been introduced. Its theoretical foundations are given in two papers. First, Ahdida and Alfonsi [2] find a methodology to simulate exactly the Wishart process for a general parameter space. Second, Kang and Kang [22] complete the scheme by proposing an expression for the conditional Laplace transform of the risky asset given the final state of the variance process. The thesis has two principle goals. First, we merge the theoretical foundations necessary to understand the exact sampling methodology and collect the corresponding proofs. Thereby, we build the basics for consecutive theoretical work, especially with respect to a necessary discussion of the numerical properties of the model. Second, we provide a prototype computational implementation. This implementation intends to be a first Monte Carlo framework for numerical experiments, testing purposes and further algorithmic improvements. It provides the tool to address future computation related research tasks. The current version is written in the MATLAB language m, and C.

Download or read book Efficient Simulation of the Double Heston Model written by Dylan Possamaï and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility models have replaced Black-Scholes model since they are able to generate a volatility smile. However, standard models fail to capture the smile slope and level movements. The double Heston model provides a more flexible approach to model the stochastic variance. This paper focuses on numerical implementation of this model. First, following the works of Lord and Kahl (2008), the analytical call option price formula given by Christoffersen et al. (2009) is corrected. Then, the discretization schemes of Andersen, Zhu and Alfonsi are numerically compared to the Euler scheme.

Download or read book Fast and Accurate Long Stepping Simulation of the Heston Stochastic Volatility Model written by Jiun Hong Chan and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Comparison of Biased Simulation Schemes for Stochastic Volatility Models written by Roger Lord and published by . This book was released on 2008 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using an Euler discretisation to simulate a mean-reverting CEV process gives rise to the problem that while the process itself is guaranteed to be nonnegative, the discretisation is not. Although an exact and efficient simulation algorithm exists for this process, at present this is not the case for the CEV-SV stochastic volatility model, with the Heston model as a special case, where the variance is modelled as a mean-reverting CEV process. Consequently, when using an Euler discretisation, one must carefully think about how to fix negative variances. Our contribution is threefold. Firstly, we unify all Euler fixes into a single general framework. Secondly, we introduce the new full truncation scheme, tailored to minimise the positive bias found when pricing European options. Thirdly and finally, we numerically compare all Euler fixes to recent quasi-second order schemes of Kahl and Jauml;ckel and Ninomiya and Victoir, as well as to the exact scheme of Broadie and Kaya. The choice of fix is found to be extremely important. The full truncation scheme outperforms all considered biased schemes in terms of bias and root-mean-squared error.

Download or read book The 4 2 Stochastic Volatility Model written by Martino Grasselli and published by . This book was released on 2016 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a new stochastic volatility model that includes, as special instances, the Heston (1993) and the 3/2 model of Heston (1997) and Platen (1997). Our model exhibits important features: first, instantaneous volatility can be uniformly bounded away from zero, and second, our model is mathematically and computationally tractable, thereby enabling an efficient pricing procedure. This called for using the Lie symmetries theory for PDEs; doing so allowed us to extend known results on Bessel processes. Finally, we provide an exact simulation scheme for the model; this is useful in view of the numerical applications.

Download or read book Gamma Expansion of the Heston Stochastic Volatility Model written by Paul Glasserman and published by . This book was released on 2011 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive an explicit representation of the transitions of the Heston stochastic volatility model and use it for fast and accurate simulation of the model. Of particular interest is the integral of the variance process over an interval, conditional on the level of the variance at the endpoints. We give an explicit representation of this quantity in terms of infinite sums and mixtures of gamma random variables. The increments of the variance process are themselves mixtures of gamma random variables. The representation of the integrated conditional variance applies the Pitman-Yor decomposition of Bessel bridges. We combine this representation with the Broadie-Kaya exact simulation method and use it to circumvent the most time-consuming step in that method.

Download or read book The Heston Model and its Extensions in Matlab and C written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2013-08-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.

Download or read book The Heston Model and Its Extensions in VBA written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2015-04-27 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical options pricing for better-informed investment decisions. The Heston Model and Its Extensions in VBA is the definitive guide to options pricing using two of the derivatives industry's most powerful modeling tools—the Heston model, and VBA. Light on theory, this extremely useful reference focuses on implementation, and can help investors more efficiently—and accurately—exploit market information to better inform investment decisions. Coverage includes a description of the Heston model, with specific emphasis on equity options pricing and variance modeling, The book focuses not only on the original Heston model, but also on the many enhancements and refinements that have been applied to the model, including methods that use the Fourier transform, numerical integration schemes, simulation, methods for pricing American options, and much more. The companion website offers pricing code in VBA that resides in an extensive set of Excel spreadsheets. The Heston model is the derivatives industry's most popular stochastic volatility model for pricing equity derivatives. This book provides complete guidance toward the successful implementation of this valuable model using the industry's ubiquitous financial modeling software, giving users the understanding—and VBA code—they need to produce option prices that are more accurate, and volatility surfaces that more closely reflect market conditions. Derivatives pricing is often the hinge on which profit is made or lost in financial institutions, making accuracy of utmost importance. This book will help risk managers, traders, portfolio managers, quants, academics and other professionals better understand the Heston model and its extensions, in a writing style that is clear, concise, transparent and easy to understand. For better pricing accuracy, The Heston Model and Its Extensions in VBA is a crucial resource for producing more accurate model outputs such as prices, hedge ratios, volatilities, and graphs.

Download or read book The Heston Stochastic Volatility Model with Piecewise Constant Parameters Efficient Calibration and Pricing of Window Barrier Options written by Daniel Guterding and published by . This book was released on 2019 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a simple and numerically efficient approach to the calibration of the Heston stochastic volatility model with piecewise constant parameters. Extending the original ansatz for the characteristic function, proposed in the seminal paper by Heston, to the case of piecewise constant parameters, we show that the resulting set of ordinary differential equations can still be integrated semi-analytically. Our numerical scheme is based on the calculation of the characteristic function using Gauss-Kronrod quadrature, additionally supplying a Black-Scholes control variate to stabilize the numerical integrals. We apply our method to the problem of calibration of the Heston model with piecewise constant parameters to the foreign exchange (FX) options market. Finally, we demonstrate cases in which window barrier option prices calculated using the Heston model with piecewise constant parameters are consistent with the market, while those calculated with a plain Heston model are not.

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.

Download or read book Derivatives Analytics with Python written by Yves Hilpisch and published by John Wiley & Sons. This book was released on 2015-06-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supercharge options analytics and hedging using the power ofPython Derivatives Analytics with Python shows you how toimplement market-consistent valuation and hedging approaches usingadvanced financial models, efficient numerical techniques, and thepowerful capabilities of the Python programming language. Thisunique guide offers detailed explanations of all theory, methods,and processes, giving you the background and tools necessary tovalue stock index options from a sound foundation. You'll find anduse self-contained Python scripts and modules and learn how toapply Python to advanced data and derivatives analytics as youbenefit from the 5,000+ lines of code that are provided to help youreproduce the results and graphics presented. Coverage includesmarket data analysis, risk-neutral valuation, Monte Carlosimulation, model calibration, valuation, and dynamic hedging, withmodels that exhibit stochastic volatility, jump components,stochastic short rates, and more. The companion website featuresall code and IPython Notebooks for immediate execution andautomation. Python is gaining ground in the derivatives analytics space,allowing institutions to quickly and efficiently deliver portfolio,trading, and risk management results. This book is the financeprofessional's guide to exploiting Python's capabilities forefficient and performing derivatives analytics. Reproduce major stylized facts of equity and options marketsyourself Apply Fourier transform techniques and advanced Monte Carlopricing Calibrate advanced option pricing models to market data Integrate advanced models and numeric methods to dynamicallyhedge options Recent developments in the Python ecosystem enable analysts toimplement analytics tasks as performing as with C or C++, but usingonly about one-tenth of the code or even less. DerivativesAnalytics with Python — Data Analysis, Models, Simulation,Calibration and Hedging shows you what you need to know tosupercharge your derivatives and risk analytics efforts.

Download or read book Monte Carlo written by George Fishman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: Apart from a thorough exploration of all the important concepts, this volume includes over 75 algorithms, ready for putting into practice. The book also contains numerous hands-on implementations of selected algorithms to demonstrate applications in realistic settings. Readers are assumed to have a sound understanding of calculus, introductory matrix analysis, and intermediate statistics, but otherwise the book is self-contained. Suitable for graduates and undergraduates in mathematics and engineering, in particular operations research, statistics, and computer science.