Nonlinear Drift And Stochastic Volatility PDF Download
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Author | : Licheng Sun |
Publisher | : |
Total Pages | : |
Release | : 2002 |
Genre | : |
ISBN | : |
Download Nonlinear Drift and Stochastic Volatility Book in PDF, ePub and Kindle
In this article I provide new evidence on the role of nonlinear drift and stochastic volatility in interest rate modeling. I compare various model specifications for the short-term interest rate using the data from five countries. I find that modeling the stochastic volatility in the short rate is far more important than specifying the shape of the drift function. The empirical support for nonlinear drift is weak with or without the stochastic volatility factor. Although a linear drift stochastic volatility model fits the international data well, I find that the level effect differs across countries.
Author | : Christian Kahl |
Publisher | : Universal-Publishers |
Total Pages | : 219 |
Release | : 2008 |
Genre | : Business & Economics |
ISBN | : 1581123833 |
Download Modelling and Simulation of Stochastic Volatility in Finance Book in PDF, ePub and Kindle
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 | : Shannon Marie Kelly |
Publisher | : |
Total Pages | : 176 |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Drift and Volatility Estimation for Stochastic Differential Equations Book in PDF, ePub and Kindle
Author | : Jun Yu |
Publisher | : |
Total Pages | : 33 |
Release | : 2013 |
Genre | : |
ISBN | : |
Download A Class of Nonlinear Stochastic Volatility Models Book in PDF, ePub and Kindle
This paper proposes a class of nonlinear stochastic volatility models based on the Box-Cox transformation which offers an alternative to the one introduced in Andersen (1994). The proposed class encompasses many parametric stochastic volatility models that have appeared in the literature, including the well known lognormal stochastic volatility model, and has an advantage in the ease with which different specifications on stochastic volatility can be tested. In addition, the functional form of transformation which induces marginal normality of volatility is obtained as a byproduct of this general way of modeling stochastic volatility. The efficient method of moments approach is used to estimate model parameters. Empirical results reveal that the lognormal stochastic volatility model is rejected for daily index return data but not for daily individual stock return data. As a consequence, the stock volatility can be well described by the lognormal distribution as its marginal distribution, consistent with the result found in a recent literature (cf Andersen et al (2001a)). However, the index volatility does not follow the lognormal distribution as its marginal distribution.
Author | : Federico M. Bandi |
Publisher | : |
Total Pages | : 43 |
Release | : 2018 |
Genre | : |
ISBN | : |
Download Nonparametric Stochastic Volatility Book in PDF, ePub and Kindle
We provide nonparametric methods for stochastic volatility modeling. Our methods allow for the joint evaluation of return and volatility dynamics with nonlinear drift and diffusion functions, nonlinear leverage effects, and jumps in returns and volatility with possibly state-dependent jump intensities, among other features. In the first stage, we identify spot volatility by virtue of jump- robust nonparametric estimates. Using observed prices and estimated spot volatilities, the second stage extracts the functions and parameters driving price and volatility dynamics from nonparametric estimates of the bivariate process' infinitesimal moments. For these infinitesimal moment estimates, we report an asymptotic theory relying on joint in-fill and long-span arguments which yields consistency and weak convergence under mild assumptions.
Author | : Robert Buff |
Publisher | : Springer Science & Business Media |
Total Pages | : 260 |
Release | : 2002-04-10 |
Genre | : Mathematics |
ISBN | : 9783540426578 |
Download Uncertain Volatility Models Book in PDF, ePub and Kindle
This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.
Author | : |
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Total Pages | : |
Release | : 1998 |
Genre | : |
ISBN | : |
Download Nonlinear filtering in stochastic volatility models Book in PDF, ePub and Kindle
Author | : Eckhard Platen |
Publisher | : |
Total Pages | : 16 |
Release | : 1997 |
Genre | : Finance |
ISBN | : |
Download A Non-linear Stochastic Volatility Model Book in PDF, ePub and Kindle
Author | : Jun Yu |
Publisher | : |
Total Pages | : 40 |
Release | : 2002 |
Genre | : Foreign exchange rates |
ISBN | : |
Download A Class of Nonlinear Stochastic Volatility Models and Its Implications on Pricing Currency Options Book in PDF, ePub and Kindle
Author | : Rafail Z. Chasʹminskij |
Publisher | : |
Total Pages | : 19 |
Release | : 2001 |
Genre | : |
ISBN | : |
Download On Estimation of the Linearized Drift for Nonlinear Stochastic Differential Equations Book in PDF, ePub and Kindle