Download or read book A Note on Hedging with Local and Stochastic Volatility Models written by Fabio Mercurio and published by . This book was released on 2016 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: The behaviour of a smile model when applied to hedging should be consistent with market evidence that asset prices and market smiles move in the same direction (Hagan et al. 2002). Local volatility models are criticized because not consistent with this desired behaviour, and this has been an important driver towards the use of stochastic volatility models.In this work we perform a simple analysis showing that, if we take into account explicitly the correlation between stochastic volatility and underlying asset which is typical of the most common stochastic volatility models, the hedging behaviour of stochastic volatility models does not always conform with the desired behaviour of a smile model in hedging.With further simple tests we show that the behaviour of local volatility and stochastic volatility models calibrated to market skew is less different than assumed in current market wisdom. Both approaches, when used consistently with model assumptions, do not show the desired behaviour in hedging, while for both models the desired behaviour is obtained in market practice by hedging techniques which are not fully consistent with rigorous model assumptions.

Download or read book Hedging Options with Local and Stochastic Volatility Models written by Leonardo Martins Nogueira and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Note on Hedging in ARCH and Stochastic Volatility Option Pricing Models written by Garcia, René and published by Montréal : CIRANO. This book was released on 1997 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Hedging with Stochastic Local Volatility written by Carol Alexander and published by . This book was released on 2004 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: The delta hedging performance of deterministic local volatility models is poor, with most studies showing that even the simple constant volatility Black-Scholes model performs better. But when the local volatility model is extended to capture stochastic dynamics for the spot volatility process, the hedge ratios change. Here, we derive the local volatility hedge ratios that are consistent with a stochastic spot volatility and show that the stochastic local volatility model is equivalent to the market model for implied volatilities. We also quantify the hedging error that arises from residual hedging uncertainty and provide an empirical example based on a stochastic normal mixture diffusion model for asset returns.

Download or read book Essays on Stochastic Local Volatility Model Option Market Making and Data driven Option Hedging written by Haoyun Tang and published by . This book was released on 2018 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Local Stochastic Volatility written by Lorenzo Bergomi and published by . This book was released on 2017 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine local-stochastic volatility models and derive a simple condition such models need to obey so that the carry P&L of a delta-hedged/vega-hedged position makes sense in a trading context.We give examples of admissible and non-admissible models and discuss the issue of the delta position in the hedge portfolio.We end with a characterization of the break-even levels of the local volatility model - itself in the admissible class.

Download or read book Strictly Local Martingales and Hedge Ratios on Stochastic Volatility Models written by Carlos Andres Sin and published by . This book was released on 1996 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hedging in Affine Stochastic Volatility Models written by Richard Vierthauer and published by . This book was released on 2010 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Implied Volatility Functions written by Bernard Dumas and published by . This book was released on 1996 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black-Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S & P 500 index options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DV option valuation model. We find that its performance is worse than that of an ad hoc Black-Scholes model with variable implied volatilities.

Download or read book Hedging Options in a GARCH Environment written by Robert F. Engle and published by . This book was released on 1994 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S & P 500 index volatility. Volatility models are compared by their ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black-Scholes (BS) delta-gamma hedge, while the BS delta-vega hedge is the least effective. The most successful volatility hedge is GARCH components delta-gamma, suggesting that the GARCH components estimate of the term structure of volatility is most accurate. The success of the BS delta-gamma hedge may be due to mispricing in the options market over the sample period.

Download or read book Stochastic volatility models Efficiency and Hedging written by and published by . This book was released on 2013 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mean Variance Hedging for Stochastic Volatility Models written by Francesca Biagini and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we discuss the tractability of stochastic volatility models for pricing and hedging options with the mean-variance hedging approach. We characterize the variance-optimal measure as the solution of an equation between Doleans exponentials; explicit examples include both models wherevolatility solves a diffusion equation and models where it follows a jump process. We further discussthe closedness of the space of strategies.

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by . This book was released on 2016 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is Chapter 2 of Stochastic Volatility Modeling, published by CRC/Chapman & Hall.In this chapter the local volatility model is surveyed as a market model for the underlying together with its associated vanilla options.First, relationships of implied to local volatilities are derived, as well as approximations for skew and curvature. Exact and approximate techniques for taking dividends into account are presented.We then turn to the dynamics of the local volatility model. We introduce the Skew Tickiness Ratio (SSR) and derive approximate formulas for the SSR and volatilities of volatilities in the local volatility model.We also examine future skews.We then consider the delta and carry P&L of a hedged option position. We derive the expression of the market-model delta of the local volatility model and discuss the relationship between sticky-strike and market-model deltas. We characterize the gamma/theta break-even levels of a hedged position and show that the local volatility model is indeed a market model.We then derive the expression of the vega-hedge portfolio.Markov-functional models are considered next.Finally, we survey the Uncertain Volatility Model and its usage.A digest summarizes key points.

Download or read book Semiparametric Modeling of Implied Volatility written by Matthias R. Fengler and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The first part is devoted to smile-consistent pricing approaches. The second part covers estimation techniques that are natural candidates to meet the challenges in implied volatility surfaces. Empirical investigations, simulations, and pictures illustrate the concepts.

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 Pricing and Hedging Exotic Options in Stochastic Volatility Models written by Zhanyu Chen and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: