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 A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics written by Matthias R. Fengler 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 VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings written by Ralf Brüggemann and published by . This book was released on 2017 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implied volatility of a European option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading times series using the vector autoregressive (VAR) framework and analyzes associated movements of these factors with movements in some macroeconomic variables of the Euro-economy.
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 A Semiparametric Factor Model for Implied Volatility Surface Dynamics written by Matthias R. Fengler and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a semiparametric factor model, which approximates the implied volatility surface (IVS) in a finite dimensional function space. Unlike standard principal component approaches typically used to reduce complexity, our approach is tailored to the degenerated design of IVS data. In particular, we only fit in the local neighborhood of the design points by exploiting the expiry effect present in option data. Using DAX index option data, we estimate the nonparametric components and a low-dimensional time series of latent factors. The modeling approach is completed by studying vector autoregressive models fitted to the latent factors.
Download or read book VAR Modeling for Dynamic Semiparametric Factors of Volatility Strings written by Ralf Brüggemann 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 VAR Modeling for Dynamic Loadings Driving Volatility Strings written by Ralf Brüggemann and published by . This book was released on 2016 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implied volatility of an option as a function of strike price and time to maturity forms a volatility surface. Traders price according to the dynamics of this high dimensional surface. Recent developments that employ semiparametric models approximate the implied volatility surface (IVS) in a finite dimensional function space, allowing for a low dimensional factor representation of these dynamics. This paper presents an investigation into the stochastic properties of the factor loading time series using the vector autoregressive (VAR) framework and analyzes the dynamic relationship of these factors with economic indicators.
Download or read book Implied Volatility String Dynamics written by Matthias R. Fengler and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Factor Models for the Volatility Surface written by Michel van der Wel and published by . This book was released on 2016 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: The implied volatility surface is the collection of volatilities implied by option contracts for different strike prices and time-to-maturity. We study factor models to capture the dynamics of this three-dimensional implied volatility surface. Three model types are considered to examine desirable features for representing the surface and its dynamics: a general dynamic factor model, restricted factor models designed to capture the key features of the surface along the moneyness and maturity dimensions, and in-between spline-based methods. Key findings are that: (i) the restricted and spline-based models are both rejected against the general dynamic factor model, (ii) the factors driving the surface are highly persistent, (iii) for the restricted models option Delta is preferred over the more often used strike relative to spot price as measure for moneyness.
Download or read book Dynamic Semiparametric Factor Models written by Szymon Borak and published by . This book was released on 2008 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Semiparametric Factor Model with a Common Break written by Likai Chen and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Semiparametric Factor Model in Applications to FMRI and Interest Rates written by Piotr Majer and published by . This book was released on 2014 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Semiparametric Factor Models in Risk Neutral Density Estimation written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Time Varying Adaptive Copulae and Dynamic Semiparametic Factor Models with Applications in Finance written by Enzo Giacomini and published by . This book was released on 2009 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Chaos Expansions in Finance written by David Nicolay and published by Springer. This book was released on 2014-12-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution.
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2009 with total page 896 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamic Semiparametric Factor Models in Risk Neutral Density Estimation written by Enzo Giacomini and published by . This book was released on 2017 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dimension reduction techniques for functional data analysis model and approximate smooth random functions by lower dimensional objects. In many applications the focus of interest lies not only in dimension reduction but also in the dynamic behaviour of the lower dimensional objects. The most prominent dimension reduction technique - functional principal components analysis - however, does not model time dependences embedded in functional data. In this paper we use dynamic semiparametric factor models (DSFM) to reduce dimensionality and analyse the dynamic structure of unknown random functions by means of inference based on their lower dimensional representation. We apply DSFM to estimate the dynamic structure of risk neutral densities implied by prices of option on the DAX stock index.
