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Author: Lorenzo Bergomi Publisher: CRC Press ISBN: 1482244071 Category : Business & Economics Languages : en Pages : 520
Book Description
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Author: Lorenzo Bergomi Publisher: CRC Press ISBN: 1482244071 Category : Business & Economics Languages : en Pages : 520
Book Description
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Author: Jean-Pierre Fouque Publisher: Cambridge University Press ISBN: 113950245X Category : Mathematics Languages : en Pages : 456
Book Description
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
Author: Christian Kahl Publisher: Universal-Publishers ISBN: 1581123833 Category : Business & Economics Languages : en Pages : 219
Book Description
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.
Author: Neil Shephard Publisher: Oxford University Press, USA ISBN: 0199257205 Category : Business & Economics Languages : en Pages : 534
Book Description
Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This work brings together some of the main papers that have influenced this field, andshows that the development of this subject has been highly multidisciplinary.
Author: Antonio Mele Publisher: Springer Science & Business Media ISBN: 1461545331 Category : Business & Economics Languages : en Pages : 156
Book Description
Stochastic Volatility in Financial Markets presents advanced topics in financial econometrics and theoretical finance, and is divided into three main parts. The first part aims at documenting an empirical regularity of financial price changes: the occurrence of sudden and persistent changes of financial markets volatility. This phenomenon, technically termed `stochastic volatility', or `conditional heteroskedasticity', has been well known for at least 20 years; in this part, further, useful theoretical properties of conditionally heteroskedastic models are uncovered. The second part goes beyond the statistical aspects of stochastic volatility models: it constructs and uses new fully articulated, theoretically-sounded financial asset pricing models that allow for the presence of conditional heteroskedasticity. The third part shows how the inclusion of the statistical aspects of stochastic volatility in a rigorous economic scheme can be faced from an empirical standpoint.
Author: Makoto Takahashi Publisher: Springer Nature ISBN: 981990935X Category : Business & Economics Languages : en Pages : 120
Book Description
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.
Author: Mr.Noureddine Krichene Publisher: International Monetary Fund ISBN: 1451854846 Category : Business & Economics Languages : en Pages : 30
Book Description
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.
Author: Emanuel Derman Publisher: John Wiley & Sons ISBN: 1118959167 Category : Business & Economics Languages : en Pages : 528
Book Description
The Volatility Smile The Black-Scholes-Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets. The Volatility Smile presents a unified treatment of the Black-Scholes-Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models. By examining the foundations, the implementation, and the pros and cons of various models, and by carefully exploring their derivations and their assumptions, readers will learn not only how to handle the volatility smile but how to evaluate and build their own financial models. Topics covered include: The principles of valuation Static and dynamic replication The Black-Scholes-Merton model Hedging strategies Transaction costs The behavior of the volatility smile Implied distributions Local volatility models Stochastic volatility models Jump-diffusion models The first half of the book, Chapters 1 through 13, can serve as a standalone textbook for a course on option valuation and the Black-Scholes-Merton model, presenting the principles of financial modeling, several derivations of the model, and a detailed discussion of how it is used in practice. The second half focuses on the behavior of the volatility smile, and, in conjunction with the first half, can be used for as the basis for a more advanced course.
Author: Lorenzo Bergomi
Author: Lorenzo Bergomi
Author: Jean-Pierre Fouque
Author: Christian Kahl
Author: Neil Shephard
Author: Jean-Pierre Fouque
Author: Antonio Mele
Author: Alan L. Lewis
Author: Makoto Takahashi
Author: Mr.Noureddine Krichene
Author: Emanuel Derman