Download or read book Application of the Heston s Stochastic Volatility Model on the Greek Stock Market written by Dimosthenis Karaflos and published by . This book was released on 2015 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study focus on applying the Heston's stochastic volatility model, to the Greek stock market, by estimating the parameters from past data. Specifically, the purpose of the study is to use the stochastic model in order to calculate the parameters of this model using the Maximum Likelihood Estimation method. In addition, the model will be used in order to manifest futures values of volatility.

Download or read book Application of the Heston Stochastic Volatility Model for Borsa Istanbul Using Impression Matrix Norm written by Ahmet Duran and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the behavior of solutions for stochastic differential equations such as the Heston stochastic volatility model. We examine the numerical solutions using Euler-Maruyama, Milstein and stochastic Runge-Kutta methods to investigate whether there is a role of the methods for different volatility cases or not, related to the impact of cumulative errors on this application. We perform simulations for different stock market conditions by using the large data set from Borsa Istanbul-100 (BIST-100) between 04.01.2007 and 31.12.2012. We use volatilities in terms of extreme values at the overlapping case when we examine initial and long term volatilities for the application of the Heston model. We also apply unit volatility based on extreme values to approximate volatilities in our analysis. We ex-amine the advantages and limitations of the model. Moreover, we introduce 3-dimensional matrix norms. Furthermore, we define market impression matrix norm as an application to the 3 dimensional matrix norms. We can benefit from it to quantify market impression approximately by means of the numerical solutions for the stochastic differential equations. Finally, we analyze the simulation results for various parameters.

Download or read book Modeling Stochastic Volatility with Application to Stock Returns written by Mr.Noureddine Krichene and published by International Monetary Fund. This book was released on 2003-06-01 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stochastic volatility model where volatility was driven solely by a latent variable called news was estimated for three stock indices. A Markov chain Monte Carlo algorithm was used for estimating Bayesian parameters and filtering volatilities. Volatility persistence being close to one was consistent with both volatility clustering and mean reversion. Filtering showed highly volatile markets, reflecting frequent pertinent news. Diagnostics showed no model failure, although specification improvements were always possible. The model corroborated stylized findings in volatility modeling and has potential value for market participants in asset pricing and risk management, as well as for policymakers in the design of macroeconomic policies conducive to less volatile financial markets.

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 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 An Empirical Analysis of Stochastic Volatility Models written by Adrien-Paul Lambillon and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to explain and apply the stochastic volatility models of Heston and GARCH to model the S&P 500 index volatility. The maximum likelihood estimate of the CIR process in the volatility equation of the Heston model and GARCH(1,1) with different underlying distributions are compared. It is shown that the model with strongest mean reversion, the CIR model, is the best volatility estimation for the overall period. For periods of volatility clustering, however, GARCH models capture the behaviour more accurately.

Download or read book The Hypergeometric Stochastic Volatility Model written by José Da Fonseca and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to introduce a new stochastic volatility model for equity derivatives. To overcome some of the well-known problems of the Heston model, and more generally of the affine models, we define a new specification for the dynamics of the stock and its volatility. Within this framework we develop all the key elements to perform the pricing of vanilla European options as well as of volatility derivatives. We clarify the conditions under which the stock price is a martingale and illustrate how the model can be implemented.

Download or read book Heston Type Stochastic Volatility with a Markov Switching Regime written by Robert J. Elliott and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct a Heston-type stochastic volatility model with a Markov switching regime to price a plain-vanilla stock option. A semi-analytic solution, which contains a matrix ODE is obtained and numerically calculated. Our model is flexible enough to provide a wide variety of volatility surfaces for the same volatility level but different regimes.

Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Analysis of the Heston Stochastic Volatility Model written by Ricardo Crisóstomo and published by . This book was released on 2016 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model, showing that relatively simple solutions can lead to fast and accurate vanilla option prices. We also perform several calibration tests, using both local and global optimization. Our analyses show that straightforward setups deliver good calibration results. All calculations are carried out in Matlab and numerical examples are included in the paper to facilitate the understanding of mathematical concepts.

Download or read book Stochastic Volatility Long Run Risks and Aggregate Stock Market Fluctuations written by Stefan Avdjiev and published by . This book was released on 2010 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimating a Local Heston Model written by Bryan Ellickson and published by . This book was released on 2018 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a new approach to modeling the volatility of stock prices that overcomes well-known problems with using realized volatility as a proxy for integrated volatility. Using high-frequency data for SPY, an exchange-traded fund that tracks the S&P 500, we estimate the parameters of a structural model of stochastic volatility for every trading day from 2007 to 2014. The estimation is successful for 46% of trading days and 71% of five-day pools. When used in conjunction with the structural model, realized volatilities are also quite effective in detecting jumps in the price or volatility process.

Download or read book A New Class of Discrete Time Stochastic Volatility Model with Correlated Errors written by Sujay Mukhoti and published by . This book was released on 2017 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining features of the relationship between the return and its volatility. Among one of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the current return is a function of the current latent volatility, which is further modeled as an auto-regressive process. In an attempt to make the SVMs more appropriate for complex realistic market behavior, a leverage parameter was introduced in the Taylor's SVM, which however led to the violation of the efficient market hypothesis (EMH, a necessary mean-zero condition for the return distribution that prevents arbitrage possibilities). Subsequently, a host of alternative SVMs had been developed and are currently in use. In this paper, we propose mean-corrections for several generalizations of Taylor's SVM that capture the complex market behavior as well as satisfy EMH. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, four real-life examples (Oil price, CITI bank stock price, Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs.

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 The Shape and Term Structure of the Index Option Smirk written by Peter Christoffersen and published by . This book was released on 2009 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art stochastic volatility models generate a quot;volatility smirkquot; that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk. However, the data indicate that the slope and the level of the smirk fluctuate largely independently. While single-factor stochastic volatility models can capture the slope of the smile, they cannot explain such largely independent fluctuations in its level and slope over time. We propose to model these movements using a two-factor stochastic volatility model. Because the factors have distinct correlations with market returns, and because the weights of the factors vary over time, the model generates stochastic correlation between volatility and stock returns. Besides providing more flexible modeling of the time variation in the smirk, the model also provides more flexible modeling of the volatility term structure. Our empirical results indicate that the model improves on the benchmark Heston model by 24% in-sample and 23% out-of-sample. The better fit results from improvements in the modeling of the term structure dimension as well as the moneyness dimension.

Download or read book The Randomised Heston Model written by Antoine (Jack) Jacquier and published by . This book was released on 2018 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a randomised version of the Heston model -- a widely used stochastic volatility model in mathematical finance -- assuming that the starting point of the variance process is a random variable. In such a system, we study the small- and large-time behaviours of the implied volatility, and show that the proposed randomisation generates a short-maturity smile much steeper ('with explosion') than in the standard Heston model, thereby palliating the deficiency of classical stochastic volatility models in short time. We precisely quantify the speed of explosion of the smile for short maturities in terms of the right tail of the initial distribution, and in particular show that an explosion rate of t^r (r in [0,1/2]) for the squared implied volatility -- as observed on market data -- can be obtained by a suitable choice of randomisation. The proofs are based on large deviations techniques and the theory of regular variations.

Download or read book Market Risk Analysis Pricing Hedging and Trading Financial Instruments written by Carol Alexander and published by John Wiley & Sons. This book was released on 2008-06-09 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by leading market risk academic, Professor Carol Alexander, Pricing, Hedging and Trading Financial Instruments forms part three of the Market Risk Analysis four volume set. This book is an in-depth, practical and accessible guide to the models that are used for pricing and the strategies that are used for hedging financial instruments, and to the markets in which they trade. It provides a comprehensive, rigorous and accessible introduction to bonds, swaps, futures and forwards and options, including variance swaps, volatility indices and their futures and options, to stochastic volatility models and to modelling the implied and local volatility surfaces. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Duration-Convexity approximation to bond portfolios, and portfolio immunization; Pricing floaters and vanilla, basis and variance swaps; Coupon stripping and yield curve fitting; Proxy hedging, and hedging international securities and energy futures portfolios; Pricing models for European exotics, including barriers, Asians, look-backs, choosers, capped, contingent, power, quanto, compo, exchange, ‘best-of’ and spread options; Libor model calibration; Dynamic models for implied volatility based on principal component analysis; Calibration of stochastic volatility models (Matlab code); Simulations from stochastic volatility and jump models; Duration, PV01 and volatility invariant cash flow mappings; Delta-gamma-theta-vega mappings for options portfolios; Volatility beta mapping to volatility indices.