Essays On American Options Pricing Under Levy Models With Stochastic Volatility And Jumps
DOWNLOAD
Download Essays On American Options Pricing Under Levy Models With Stochastic Volatility And Jumps PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Essays On American Options Pricing Under Levy Models With Stochastic Volatility And Jumps book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Essays On American Options Pricing Under Levy Models With Stochastic Volatility And Jumps
DOWNLOAD
Author : Ye Chen
language : en
Publisher:
Release Date : 2019
Essays On American Options Pricing Under Levy Models With Stochastic Volatility And Jumps written by Ye Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
In ``A Multi-demensional Transform for Pricing American Options Under Stochastic Volatility Models", we present a new transform-based approach for pricing American options under low-dimensional stochastic volatility models which can be used to construct multi-dimensional path-independent lattices for all low-dimensional stochastic volatility models given in the literature, including SV, SV2, SVJ, SV2J, and SVJ2 models. We demonstrate that the prices of European options obtained using the path-independent lattices converge rapidly to their true prices obtained using quasi-analytical solutions. Our transform-based approach is computationally more efficient than all other methods given in the literature for a large class of low-dimensional stochastic volatility models. In ``A Multi-demensional Transform for Pricing American Options Under Levy Models", We extend the multi-dimensional transform to Levy models with stochastic volatility and jumps in the underlying stock price process. Efficient path-independent tree can be constructed for both European and American options. Our path-independent lattice method can be applied to almost all Levy models in the literature, such as Merton (1976), Bates (1996, 2000, 2006), Pan (2002), the NIG model, the VG model and the CGMY model. The numerical results show that our method is extemly accurate and fast. In ``Empirical performance of Levy models for American Options", we investigate in-sample fitting and out-of-sample pricing performance on American call options under Levy models. The drawback of the BS model has been well documented in the literatures, such as negative skewness with excess kurtosis, fat tail, and non-normality. Therefore, many models have been proposed to resolve known issues associated the BS model. For example, to resolve volatility smile, local volatility, stochastic volatility, and diffusion with jumps have been considered in the literatures; to resolve non-normality, non-Markov processes have been considered, e.g., Poisson process, variance gamma process, and other type of Levy processes. One would ask: what is the gain from each of the generalized models? Or, which model is the best for option pricing? We address these problems by examining which model results in the lowest pricing error for American style contracts. For in-sample analysis, the rank (from best to worst) is Pan, CGMYsv, VGsv, Heston, CGMY, VG and BS. And for out-of-sample pricing performance, the rank (from best to worst) is CGMYsv, VGsv, Pan, Heston, BS, VG, and CGMY. Adding stochastic volatility and jump into a model improves American options pricing performance, but pure jump models are worse than the BS model in American options pricing. Our empirical results show that pure jump model are over-fitting, but not improve American options pricing when they are applied to out-of-sample data.
American Options In Levy Models With Stochastic Volatility
DOWNLOAD
Author : Svetlana Boyarchenko
language : en
Publisher:
Release Date : 2008
American Options In Levy Models With Stochastic Volatility written by Svetlana Boyarchenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in the sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of a Levy process with the intensity coefficient driven by the square root process with embedded jumps is derived. Numerical examples corroborate the general result about a gap between strike and early exercise boundary at expiry, in a neighborhood of r=0, in the presence of jumps.
Exotic Option Pricing And Advanced L Vy Models
DOWNLOAD
Author : Andreas Kyprianou
language : en
Publisher: John Wiley & Sons
Release Date : 2006-06-14
Exotic Option Pricing And Advanced L Vy Models written by Andreas Kyprianou and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-14 with Business & Economics categories.
Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
The Impact Of Jumps On American Option Pricing
DOWNLOAD
Author : Boda Kang
language : en
Publisher:
Release Date : 2019
The Impact Of Jumps On American Option Pricing written by Boda Kang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
This paper analyzes the importance of asset and volatility jumps in American option pricing models. Using the Heston (1993) stochastic volatility model with asset and volatility jumps and the Hull and White (1987) short rate model, American options are numerically evaluated by the Method of Lines. The calibration of these models to S&P 100 American options data reveals that jumps, especially asset jumps, play an important role in improving the models' ability to fit market data. Further, asset and volatility jumps tend to lift the free boundary, an effect that augments during volatile market conditions, while the additional volatility jumps marginally drift down the free boundary. As markets turn more volatile and exhibit jumps, American option holders become more prudent with their exercise decisions, especially as maturity of the options approaches.
Essays On Volatilities Implied By Option Prices
DOWNLOAD
Author : Aamir Mohammad Sheikh
language : en
Publisher:
Release Date : 1987
Essays On Volatilities Implied By Option Prices written by Aamir Mohammad Sheikh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
American Options In L Vy Models With Stochastic Interest Rates
DOWNLOAD
Author : Svetlana Boyarchenko
language : en
Publisher:
Release Date : 2008
American Options In L Vy Models With Stochastic Interest Rates written by Svetlana Boyarchenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. An explicit algorithm for the case of positive stochastic interest rates driven by a process of the Ornstein-Uhlenbeck type is derived. Efficiency of the method is illustrated with numerical examples.
Option Pricing With Long Memory Stochastic Volatility Models
DOWNLOAD
Author : Zhigang Tong
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2013
Option Pricing With Long Memory Stochastic Volatility Models written by Zhigang Tong and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance.
American Options In Regime Switching L Vy Models With Non Semibounded Stochastic Interest Rates
DOWNLOAD
Author : Svetlana Boyarchenko
language : en
Publisher:
Release Date : 2008
American Options In Regime Switching L Vy Models With Non Semibounded Stochastic Interest Rates written by Svetlana Boyarchenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. Contrary to the earlier version of the method, the interest rate may assume non-positive values. As applications, explicit algorithms for Vasicek and Black's models with jumps are derived. Numerical examples show that the option prices in these two models are very close.
Essays On Market Microstructure And Options
DOWNLOAD
Author : Stkewart James Mayhew
language : en
Publisher:
Release Date : 1996
Essays On Market Microstructure And Options written by Stkewart James Mayhew and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Essays In Volatility And Stochastic Volatility Option Pricing Models
DOWNLOAD
Author : İnanç Kırgız
language : en
Publisher:
Release Date : 2001
Essays In Volatility And Stochastic Volatility Option Pricing Models written by İnanç Kırgız and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Financial futures categories.