Download or read book Notes On Stochastic Rates Dividends Volatilities in an Equity Framework written by Lionel Viet and published by . This book was released on 2012 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 1 - Black-Scholes formulas are consistent with a diffusion in the respective forward neutral probability.Part 2 - Mixing Forward Neutral Probabilities for different maturities, we construct a probability more natural for non european payoffs, different from the Risk Neutral measure, that we call the Pricing Probability.Part 3 - Writing the Radon-Nikodym derivative for changing measure to the Pricing Probability, and the modified HJM relationship.Part 4 - We use a simple Ho amp; Lee model to get a sense of how the path-dependent hybrid terms impact the Stock diffusions. Due to hybrid effects, BS vols term structure is usually increasing.Part 5 - The Pricing Probability seems to be the natural Probability to be used to price Equity-Linked Structures with any kind of Hybrid Risks - ie all non Strictly European Structures. The alternative - working in the Risk Neutral Probability - would necessitate to recalibrate all volatility, correlation parameters from the Black / Black Scholes world (Forward Neutral Probabilities) to the Risk Neutral world.Part 6 - Some examples of Interest Rate models.Part 7 - Stochastic Dividends diffusions. Ho amp; Lee example.Part 8 - Cross-Currency framework. Ho amp; Lee example.Part 9 - Risky Curve Diffusions in the Survival Neutral Probabilities.Analogy with the Currency Quanto World.A quick look at Counterparty Risk and CVA adjustments.Part 10 - Multi-Underlying Framework. Ho amp; Lee example. Due to hybrid effects, BS correlations term structure is usually increasing.Part 11 - Stochastic Volatility Framework.A statistical bias between vol of realized vols and vol of implied vols.Variance Swaps on Spots, Variances Swaps on Forwards, European Options.Part 12 - Natural parametrizations of volsurfaces coherent with vol dynamics and risks, based on vol, volvol and correl spot/vol breakevens.Historical backtests of implied vs realized breakevens.Generalization with 6 parameters per Maturity.Part 13 - Correlation Skew and Stochastic Volatility.We show that we can calibrate a basket skew independently of individual skews without introducing a spot-dependent correlation: this is typically the case when individual vols move more with the basket spot than with individual spots.

Download or read book Stochastic Proportional Dividends written by Hans Buehler and published by . This book was released on 2018 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by recently increased interest in trading derivatives on dividends, we present a simple, yet efficient equity stock price model with discrete stochastic proportional dividends.The model has a closed form for European option pricing and can therefore be calibrated efficiently to vanilla options on the equity. It can also be simulated efficiently with Monte-Carlo and has fast analytics to aid the pricing of derivatives on dividends.While its efficiency makes the model very appealing, it has the twin drawbacks that dividends in this model can become negative, and that it does not price in any skew on either dividends or the stock price.We present the model and also discuss various extensions to stochastic interest rates, local volatility and jumps.(The 2012 revision corrects a minor mistake in the original paper).

Download or read book An Analysis of the Equity Local Volatility Model with Affine Dividends written by Ghislain Vong and published by . This book was released on 2018 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This note discusses the impact of dividend modelling on the pricing of equity exotic derivatives under a local volatility model. It explains how the level of the implied local variance is adjusted as the contribution of proportional dividends is increased and characterises the impact of the mixture specification on the forward transition probability of the equity spot process.

Download or read book Can Standard Preferences Explain the Prices of Out of the Money S P 500 Put Options written by Luca Benzoni and published by . This book was released on 2005 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prior to the stock market crash of 1987, Black-Scholes implied volatilities of S & P 500 index options were relatively constant across moneyness. Since the crash, however, deep out-of-the-money S & P 500 put options have become 'expensive' relative to the Black-Scholes benchmark. Many researchers (e.g., Liu, Pan and Wang (2005)) have argued that such prices cannot be justified in a general equilibrium setting if the representative agent has 'standard preferences' and the endowment is an i.i.d. process. Below, however, we use the insight of Bansal and Yaron (2004) to demonstrate that the 'volatility smirk' can be rationalized if the agent is endowed with Epstein-Zin preferences and if the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. We identify a realistic calibration of the model that simultaneously matches the empirical properties of dividends, the equity premium, the prices of both at-the-money and deep out-of-the-money puts, and the level of the risk-free rate. A more challenging question (that to our knowledge has not been previously investigated) is whether one can explain within a standard preference framework the stark regime change in the volatility smirk that has maintained since the 1987 market crash. To this end, we extend the model to a Bayesian setting in which the agent updates her beliefs about the average jump size in the event of a jump. Note that such beliefs only update at crash dates, and hence can explain why the volatility smirk has not diminished over the last eighteen years. We find that the model can capture the shape of the implied volatility curve both pre- and post-crash while maintaining reasonable estimates for expected returns, price-dividend ratios, and risk-free rates.

Download or read book The Volatility Smile written by Emanuel Derman and published by John Wiley & Sons. This book was released on 2016-09-06 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Multiscale Stochastic Volatility for Equity Interest Rate and Credit Derivatives written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2011-09-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Equity Modeling with Stochastic Dividends written by Hamza Guennoun and published by . This book was released on 2017 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we show how to incorporate exactly discrete stochastic dividends in (hybrid) local stochastic volatility models. Our algorithm is illustrated by various numerical examples. We also specify a dividend model which is easy simulable and consistent with the market dividend smile.

Download or read book Pricing Long Maturity Equity and FX Derivatives with Stochastic Interest Rates and Stochastic Volatility written by Alexander van Haastrecht and published by . This book was released on 2011 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we extend the stochastic volatility model of Schouml;bel and Zhu (1999) by including stochastic interest rates. Furthermore we allow all driving model factors to be instantaneously correlated with each other, i.e. we allow for a correlation between the instantaneous interest rates, the volatilities and the underlying stock returns. By deriving the characteristic function of the log-asset price distribution, we are able to price European stock options in closed-form by Fourier inversion. Furthermore we present a Foreign Exchange generalization and show how the pricing of Forward-starting options like cliquets can be performed. Additionally we discuss the practical implementation of these new models.

Download or read book Multiscale Stochastic Volatility for Equity Interest Rate and Credit Derivatives written by Jean-Pierre Fouque and published by . This book was released on 2014-05-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consolidate and extend ideas from their previous book. Ideal for practitioners and as a graduate-level textbook.

Download or read book Advanced Equity Derivatives written by Sebastien Bossu and published by John Wiley & Sons. This book was released on 2014-05-19 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Advanced Equity Derivatives: Volatility and Correlation, Sébastien Bossu reviews and explains the advanced concepts used for pricing and hedging equity exotic derivatives. Designed for financial modelers, option traders and sophisticated investors, the content covers the most important theoretical and practical extensions of the Black-Scholes model. Each chapter includes numerous illustrations and a short selection of problems, covering key topics such as implied volatility surface models, pricing with implied distributions, local volatility models, volatility derivatives, correlation measures, correlation trading, local correlation models and stochastic correlation. The author has a dual professional and academic background, making Advanced Equity Derivatives: Volatility and Correlation the perfect reference for quantitative researchers and mathematically savvy finance professionals looking to acquire an in-depth understanding of equity exotic derivatives pricing and hedging.

Download or read book Financial Economics written by Antonio Mele and published by MIT Press. This book was released on 2022-11-22 with total page 1147 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive reference for financial economics, balancing theoretical explanations, empirical evidence, and the practical relevance of knowledge in the field. This volume offers a comprehensive, integrated treatment of financial economics, tracking the major milestones in the field and providing methodological tools. Doing so, it balances theoretical explanations, empirical evidence, and practical relevance. It illustrates nearly a century of theoretical advances with a vast array of models, showing how real phenomena (and, at times, market practice) have helped economists reformulate existing theories. Throughout, the book offers examples and solved problems that help readers understand the main lessons conveyed by the models analyzed. The book provides a unique and authoritative reference for the field of financial economics. Part I offers the foundations of the field, introducing asset evaluation, information problems in asset markets and corporate finance, and methods of statistical inference. Part II explains the main empirical facts and the challenges these pose for financial economists, which include excess price volatility, market liquidity, market dysfunctionalities, and the countercyclical behavior of market volatility. Part III covers the main instruments that protect institutions against the volatilities and uncertainties of capital markets described in part II. Doing so, it relies on models that have become the market standard, and incorporates practices that emerged from the 2007–2008 financial crisis.

Download or read book Stochastic Analysis with Financial Applications written by Arturo Kohatsu-Higa and published by Springer Science & Business Media. This book was released on 2011-07-22 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.

Download or read book The Skewness Premium and the Asymmetric Volatility Puzzle written by Canlin Li and published by . This book was released on 2004 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper uses a general equilibrium model to study the source and reward of asymmetric volatility or skewness of market returns in an exchange economy. In particular, the dividend growth rate is modeled as a stochastic volatility process and the representative agent is characterized by Epstein-Zin preferences. The equilibrium equity premium, risk-free rate, and asymmetric volatility (measured by the negative correlation between the market return and its volatility) are derived endogenously. It is shown that the equity premium has three components: the first two components parallel those in the Intertemporal CAPM, while the last one is 'new'. It reflects the part of excess returns required by investors to take on the asymmetric volatility or negative skewness risk. The paper then uses the Efficient Method of Moments to estimate the stochastic volatility model of the dividend growth rate and uses the estimated process to study the equity premium, the skewness premium, the risk-free rate, and asymmetric volatility under various values of the risk aversion coefficient and elasticity of intertemporal substitution. It is shown that the skewness premium can be as high as 1.2% annually in real terms. However, under conventional levels of risk aversion and elasticity of intertemporal substitution, the asymmetric volatility generated by the model is much smaller than that observed in the data and hence results in the asymmetric volatility 'puzzle'

Download or read book Value Of Uncertainty The Dealing With Risk In The Equity Derivatives Market written by George J Kaye and published by World Scientific Publishing Company. This book was released on 2012-11-16 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with the extraordinary growth in the derivatives market over the last decade, the impact of model choice, and model parameter usage, has become a major source of valuation uncertainty. This book concentrates on equity derivatives and charts, step by step, how key assumptions on the dynamics of stocks impact on the value of exotics. The presentation is technical, but maintains a strong focus on intuition and practical application./a

Download or read book Systemic Contingent Claims Analysis written by Mr.Andreas A. Jobst and published by International Monetary Fund. This book was released on 2013-02-27 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt: The recent global financial crisis has forced a re-examination of risk transmission in the financial sector and how it affects financial stability. Current macroprudential policy and surveillance (MPS) efforts are aimed establishing a regulatory framework that helps mitigate the risk from systemic linkages with a view towards enhancing the resilience of the financial sector. This paper presents a forward-looking framework ("Systemic CCA") to measure systemic solvency risk based on market-implied expected losses of financial institutions with practical applications for the financial sector risk management and the system-wide capital assessment in top-down stress testing. The suggested approach uses advanced contingent claims analysis (CCA) to generate aggregate estimates of the joint default risk of multiple institutions as a conditional tail expectation using multivariate extreme value theory (EVT). In addition, the framework also helps quantify the individual contributions to systemic risk and contingent liabilities of the financial sector during times of stress.

Download or read book A Benchmark Approach to Quantitative Finance written by Eckhard Platen and published by Springer Science & Business Media. This book was released on 2006-10-28 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: A framework for financial market modeling, the benchmark approach extends beyond standard risk neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. This book presents the necessary mathematical tools, followed by a thorough introduction to financial modeling under the benchmark approach, explaining various quantitative methods for the fair pricing and hedging of derivatives.

Download or read book Complex Systems in Finance and Econometrics written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.