Download or read book DSFM Fitting of Implied Volatility Surfaces written by Szymon Borak and published by . This book was released on 2017 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implied volatility became one of the key issues in modern quantitative finance, since the plain vanilla option prices contain vital information for pricing and hedging of exotic and illiquid options. European plain vanilla options are nowadays widely traded, which results in a great amount of high-dimensional data especially on an intra day level. The data reveal a degenerated string structure. Dynamic Semiparametric Factor Models (DSFM) are tailored to handle complex, degenerated data and yield low dimensional representation of the implied volatility surface (IVS). We discuss estimation issues of the model and apply it to DAX option prices.
Download or read book DSFM Fitting of Implied Volatility Surfaces written by Szymon Borak and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fitting Local Volatility Analytic And Numerical Approaches In Black scholes And Local Variance Gamma Models written by Andrey Itkin and published by World Scientific. This book was released on 2020-01-22 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black-Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.This book was written with the purpose of presenting new results previously developed in a series of papers and explaining them consistently, starting from the general concept of Dupire, Derman and Kani and then concentrating on various extensions proposed by the author and his co-authors. This volume collects all the results in one place, and provides some typical examples of the problems that can be efficiently solved using the proposed methods. This also results in a faster calibration of the local and implied volatility surfaces as compared to standard approaches.The methods and solutions presented in this volume are new and recently published, and are accompanied by various additional comments and considerations. Since from the mathematical point of view, the level of details is closer to the applied rather than to the abstract or pure theoretical mathematics, the book could also be recommended to graduate students with majors in computational or quantitative finance, financial engineering or even applied mathematics. In particular, the author used to teach some topics of this book as a part of his special course on computational finance at the Tandon School of Engineering, New York University.
Download or read book Volatility Surfaces written by Wulin Suo and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Implied volatilities are frequently used to quote the prices of options. The implied volatility of a European option on a particular asset as a function of strike price and time to maturity is known as the asset's volatility surface. Traders monitor movements in volatility surfaces closely. In this paper we develop a no-arbitrage condition for the evolution of a volatility surface. We examine a number of rules of thumb used by traders to manage the volatility surface and test whether they are consistent with the no-arbitrage condition and with data on the trading of options on the S&P 500 taken from the over-the-counter market. Finally we estimate the factors driving the volatility surface in a way that is consistent with the no-arbitrage condition.
Download or read book Analysis of Implied Volatility Surfaces written by Marina Schnellen and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Dynamics of Implied Volatility Surfaces written by Les Clewlow and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the papers of Dupire (1992) and Derman and Kani (1997), we want to investigate the number of shocks that move the whole implied volatility surface, their interpretation and their correlation with percentage changes in the underlying asset. This work differs from Skiadopoulos, Hodges and Clewlow (1998) in which they looked at the dynamics of smiles for a given maturity bucket. We look at daily changes in implied volatilities under two different metrics: the strike metric and the moneyness metric. Since we are dealing with a three dimensional problem, we fix ranges of days to maturity, we pool them together and we apply the Principal Components Analysis (PCA) to the changes in implied volatilities over time across both the strike (moneyness) metric and the pooled ranges of days to maturity. We find similar results for both metrics. Two shocks explain the movements of the volatility surface, the first shock being interpreted as a shift, while the second one has a Z-shape. The sign of the correlation of the first shock with percentage changes in the underlying asset depends on the metric that we look at, while the sign is positive under both metrics regarding the second shock. The results suggest that the number of shocks, their interpretation and the sign of their correlation with changes in the underlying asset is the same for the whole implied volatility surface as it is for the smile corresponding to a fixed maturity bucket.
Download or read book The Volatility Sneer written by D. Clive Thompson and published by . This book was released on 1997 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fitting Local Volatility written by Andrey Itkin and published by . This book was released on 2020 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Implied volatility surfaces written by Robert G. Tompkins and published by . This book was released on 1999 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Implied volatility surfaces written by Robert G. Tompkins and published by . This book was released on 1999 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics written by Matthias R. Fengler and published by . This book was released on 2017 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: A primary goal in modelling the implied volatility surface (IVS) for pricing and hedging aims at reducing complexity. For this purpose one fits the IVS each day and applies a principal component analysis using a functional norm. This approach, however, neglects the degenerated string structure of the implied volatility data and may result in a modelling bias. We propose a dynamic semiparametric factor model (DSFM), which approximates the IVS in a finite dimensional function space. The key feature is that we only fit in the local neighborhood of the design points. Our approach is a combination of methods from functional principal component analysis and backfitting techniques for additive models. The model is found to have an approximate 10% better performance than a sticky moneyness model. Finally, based on the DSFM, we devise a generalized vega-hedging strategy for exotic options that are priced in the local volatility framework. The generalized vega-hedging extends the usual approaches employed in the local volatility framework.
Download or read book Dynamics of the Implied Volatility Surface written by Jacinto Marabel Romo and published by . This book was released on 2014 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: I perform a regression analysis to test two of the most famous heuristic rules existing in the literature about the behavior of the implied volatility surface. These rules are the sticky delta rule and the sticky strike rule. I present a new specification to test the sticky strike rule, which allows for dynamics in the implied volatility surface. In the empirical application I use monthly implied volatility surfaces corresponding to the IBEX 35 index. The estimation results show that the extended specification for the sticky strike rule presented in this article represents better the behavior of the implied volatility under this rule. Furthermore, there is not one rule which is the most appropriate at all times to explain the evolution of implied volatility surface. Depending on the market situation a rule may be more appropriate than another one. In particular, when the underlying asset displays trend, the sticky delta rule tends to prevail against the sticky strike rule. Conversely, when the underlying asset moves in range, then the sticky strike rule tends to predominate.
Download or read book Stochastic Models of Implied Volatility Surfaces written by Rama Cont and published by . This book was released on 2002 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a market-based approach to the modelling of implied volatility, in which the implied volatility surface is directly used as the state variable to describe the joint evolution of market prices of options and their underlying asset. We model the evolution of an implied volatility surface by representing it as a randomly fluctuating surface driven by a finite number of orthogonal random factors. Our approach is based on a Karhunen-Loeve decomposition of the daily variations of implied volatilities obtained from market data on SP500 and DAX options.We illustrate how this approach extends and improves the accuracy of the well-known 'sticky moneyness' rule used by option traders for updating implied volatilities. Our approach gives a justification for the use of 'Vegas' for measuring volatility risk and provides a decomposition of volatility risk as a sum of independent contributions from empirically identifiable factors.
Download or read book Implied Volatility Surface Reconstruction for Energy Markets written by Mikhail Vladimirovich Deryabin and published by . This book was released on 2014 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this note we describe and compare two methodologies for calculating implied volatility of commodity prices, given the market prices of options on futures or implied volatilities, and a forward curve. The first methodology is fitting an exponential mean-reversion jump-diffusion model to the data, the second one is using a particular parameterisation of the surface that ensures no-arbitrage conditions. We use NYMEX data on WTI European-type oil options on futures as an example.
Download or read book Modeling the Dynamics of Implied Volatility Surfaces written by Ihsan Badshah and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this study is to model implied volatility surfaces and identify risk factors that account for most of the randomness in the volatility surfaces. The approach is similar to that of the Dumas, Fleming and Whaley (DFW) (1998) study. We use moneyness in implied forward price and out-of-the-money put-call options on the FTSE 100 stock index. After adjustments, a nonlinear parametric optimization technique is used to estimate different DFW models to characterize and produce smooth implied volatility surfaces. Next, principal component analysis is applied to the implied volatility surfaces to extract principal components that account for most of the dynamics in the shape of the surfaces. We then estimate and obtain smooth implied volatility surfaces with the parametric models that account for both smirk(skew) and time to maturity. We find the constant volatility model fails to explain the variations in the surfaces. However, the first three principal components (or factors) can explain about 69-88% of the variances in the implied volatility surfaces: in which on average 56% explains by the level factor, 15% by the term structure factor, and additional 7% by the jump-fear factor. The applications of our study can be in options trading, hedging of derivatives positions, risk management of options, and policy making.
Download or read book Forecasting Implied Volatility Surfaces written by Francesco Audrino and published by . This book was released on 2007 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Deformation of Implied Volatility Surfaces written by Rama Cont and published by . This book was released on 2001 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
