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Author : Evashun Pillay
Publisher :
ISBN 13 :
Total Pages : 115 pages
Book Rating : 4.:/5 (71 download)
Download or read book FFT Based Option Pricing Under Mean Reversion, Jumps and Stochastic Volatility written by Evashun Pillay and published by . This book was released on 2009 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Artur Sepp
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (13 download)
Download or read book Pricing European-Style Options Under Jump Diffusion Processes with Stochastic Volatility written by Artur Sepp and published by . This book was released on 2014 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper surveys the developments in the finance literature with respect to applying the Fourier transform for option pricing under affine jump-diffusions. We provide a broad description of the issues and a detailed summary of the main points and features of the models proposed. First, we consider a wide class of affine jump-diffusions proposed for the asset price dynamics: jump-diffusions, diffusions with stochastic volatility, jump-diffusions with stochastic volatility, and jump-diffusions with stochastic volatility and jump intensity. Next we apply the Fourier transform for solving the problem of European option pricing under these price processes. We present two solution methods: the characteristic formula and the Black-Scholes-style formula. Finally, we discuss numerical implementation of pricing formulas and apply the considered processes for modeling the DAX options volatility surface.
Author : Hoi Ying Wong
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (129 download)
Download or read book Option Pricing with Mean Reversion and Stochastic Volatility written by Hoi Ying Wong and published by . This book was released on 2009 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many underlying assets of option contracts, such as currencies, commodities, energy, temperature and even some stocks, exhibit both mean reversion and stochastic volatility. This paper investigates the valuation of options when the underlying asset follows a mean-reverting lognormal process with stochastic volatility. A closed-form solution is derived for European options by means of Fourier transform. The proposed model allows the option pricing formula to capture both the term structure of futures prices and the market implied volatility smile within a unified framework. A bivariate trinomial lattice approach is introduced to value path-dependent options with the proposed model. Numerical examples using European options, American options and barrier options demonstrate the use of the model and the quality of the numerical scheme.
Author : Irena Andreevska
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (297 download)
Download or read book Mathematical Modeling and Analysis of Options with Jump-diffusion Volatility written by Irena Andreevska and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Several existing pricing models of financial derivatives as well as the effects of volatility risk are analyzed. A new option pricing model is proposed which assumes that stock price follows a diffusion process with square-root stochastic volatility. The volatility itself is mean-reverting and driven by both diffusion and compound Poisson process. These assumptions better reflect the randomness and the jumps that are readily apparent when the historical volatility data of any risky asset is graphed. The European option price is modeled by a homogeneous linear second-order partial differential equation with variable coefficients. The case of underlying assets that pay continuous dividends is considered and implemented in the model, which gives the capability of extending the results to American options. An American option price model is derived and given by a non-homogeneous linear second order partial integro-differential equation. Using Fourier and Laplace transforms an exact closed-form solution for the price formula for European call/put options is obtained.
Author : Fernanda D'Ippoliti
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (13 download)
Download or read book Exact and Approximated Option Pricing in a Stochastic Volatility Jump-Diffusion Model written by Fernanda D'Ippoliti and published by . This book was released on 2014 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a stochastic volatility jump-diffusion model for option pricing with contemporaneous jumps in both spot return and volatility dynamics. The model admits, in the spirit of Heston, a closed-form solution for European-style options. To evaluate more complex derivatives for which there is no explicit pricing expression, such as barrier options, a numerical methodology, based on an “exact algorithm” proposed by Broadie and Kaya, is applied. This technique is called exact as no discretisation of dynamics is required. We end up testing the goodness of our methodology using, as real data, prices and implied volatilities from the DJ Euro Stoxx 50 market and providing some numerical results for barrier options and their Greeks.
Author : Kaushik I. Amin
Publisher :
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.3/5 ( download)
Download or read book Option Valuation with Systematic Stochastic Volatility written by Kaushik I. Amin and published by . This book was released on 1992 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christian Hafner
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (666 download)
Download or read book Simple Approximations for Option Pricing Under Mean Reversion and Stochastic Volatility written by Christian Hafner and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jianwei Zhu
Publisher : Springer Science & Business Media
ISBN 13 : 3642018084
Total Pages : 338 pages
Book Rating : 4.6/5 (42 download)
Download or read book Applications of Fourier Transform to Smile Modeling written by Jianwei Zhu and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy ́ jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene?t from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory.
Author : Mohammad Yousef Akhavein Sohrabi
Publisher :
ISBN 13 :
Total Pages : 83 pages
Book Rating : 4.:/5 (827 download)
Download or read book Option Pricing Under Regime Switching (analytical, PDE, and FFT Methods) written by Mohammad Yousef Akhavein Sohrabi and published by . This book was released on 2011 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples.
Author : Guoqing Yan
Publisher :
ISBN 13 : 9781109872637
Total Pages : 114 pages
Book Rating : 4.8/5 (726 download)
Download or read book Option Pricing for a Stochastic-volatility Jump-diffusion Model written by Guoqing Yan and published by . This book was released on 2006 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the accurate and fast European option pricing formulas, we calibrate the models to S&P 500 Index option quotes by least squares method. Spot variance and structural parameters for different models including Black-Scholes, Stochastic-Volatility. SVJD-Uniform, SVJD-Normal, SVJD-DbExp are estimated. Fitting performance of different models are compared and our proposed SVJD-Uniform model is found to fit the market data the best.
Author : Jianwei Zhu
Publisher : Springer Science & Business Media
ISBN 13 : 9783540679165
Total Pages : 188 pages
Book Rating : 4.6/5 (791 download)
Download or read book Modular Pricing of Options written by Jianwei Zhu and published by Springer Science & Business Media. This book was released on 2000 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The sound modeling of the smile effect is an important issue in quantitative finance as, for more than a decade, the Fourier transform has established itself as the most efficient tool for deriving closed-form option pricing formulas in various model classes. This book describes the applications of the Fourier transform to the modeling of volatility smile, followed by a comprehensive treatment of option valuation in a unified framework, covering stochastic volatilities and interest rates, Poisson and Levy jumps, including various asset classes such as equity, FX and interest rates, as well as various numberical examples and prototype programming codes. Readers will benefit from this book not only by gaining an overview of the advanced theory and the vast range of literature on these topics, but also by receiving first-hand feedback on the practical applications and implementations of the theory. The book is aimed at financial engineers, risk managers, graduate students and researchers.
Author : Aytekin Sari
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book Stochastic Volatility and Jump Diffusion Option Pricing Model written by Aytekin Sari and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexander Pitkin
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (119 download)
Download or read book High-order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Jump-diffusion Models written by Alexander Pitkin and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Louis O. Scott
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (753 download)
Download or read book Pricing Stock Options in a Jump-diffusion Model with Stochastic Volatility and Interest Rates written by Louis O. Scott and published by . This book was released on 1995 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chun-Sung Huang
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (13 download)
Download or read book Highly Efficient Option Valuation Under the Double Jump Framework with Stochastic Volatility and Jump Intensity Based on Shannon Wavelet Inverse Fourier Technique written by Chun-Sung Huang and published by . This book was released on 2017 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we explore the highly efficient valuation of financial options under a double exponential jump framework, with stochastic volatility and jump intensity. In particular, we investigate both the accuracy and efficiency of pricing options using the novel Shannon wavelet inverse Fourier technique (SWIFT). Resulting prices are compared to the benchmark Fast Fourier Transform (FFT) and, its more recent alternative, the Fourier Cosine (COS) expansion prices. We demonstrate that not only is the SWIFT method more efficient, it is also accurate with exponential error convergence for both call and put valuations. Finally, further evidence of model robustness and stability is presented through a price sensitivity analysis, where we investigate the significant impact of changing model parameters to the resulting option values.
Author : Henrik Andersson
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (129 download)
Download or read book A Mean-Reverting Stochastic Volatility Option-Pricing Model with an Analytic Solution written by Henrik Andersson and published by . This book was released on 2002 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we derive a closed form approximation to a stochastic volatility option-pricing model and propose a variant of EGARCH for parameter estimation. The model thereby provides a consistent approach to the problem of option pricing and parameter estimation. Using Swedish stocks, the model provides a good fit to the heteroscedasticity prevalent in the time-series. The stochastic volatility model also prices options on the underlying stock more accurately than the traditional Black-Scholes formula. This result holds for both historic and implied volatility. A large part of the volatility smile that is observed for options of different maturity and exercise prices is thereby explained.
Author : Matthew James Lorig
Publisher :
ISBN 13 : 9781124885568
Total Pages : 187 pages
Book Rating : 4.8/5 (855 download)
Download or read book Option-pricing with Fast Mean-reverting Stochastic Volatility Models written by Matthew James Lorig and published by . This book was released on 2011 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1J.-P. Fouque, G. Papanicolaou, and R. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, 2000.
