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Titlebook: Applications of Fourier Transform to Smile Modeling; Theory and Implement Jianwei Zhu Book 2010Latest edition Springer-Verlag Berlin Heidel

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期刊全称Applications of Fourier Transform to Smile Modeling
期刊简称Theory and Implement
影响因子2023Jianwei Zhu
视频video
学科分类Springer Finance
图书封面Titlebook: Applications of Fourier Transform to Smile Modeling; Theory and Implement Jianwei Zhu Book 2010Latest edition Springer-Verlag Berlin Heidel
影响因子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
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Applications of Fourier Transform to Smile Modeling978-3-642-01808-4Series ISSN 1616-0533 Series E-ISSN 2195-0687
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Marian Brezina,Jonathan Hu,Ray Tuminaro and begin with the next chapter directly. A Brownian motion is an elemental building-block in modeling the dynamics of stock returns, and correspondingly the geometric Brownian motion as an exponential function of Brownian motion is the simplest and most popular process for stock prices, on which t
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Marian Brezina,Jonathan Hu,Ray Tuminarock price is analytically unknown. To express (quasi-) closed-form exercise probabilities and valuation formula, characteristic functions of the underlying stock returns (logarithms) are proven to be not only a powerful and convenient tool to achieve analytical tractability, but also a large accommod
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Marian Brezina,Jonathan Hu,Ray Tuminarostic volatility models is crucial for a sound performance of the pricing engine and the model calibration, and includes some different aspects: the numerical integration of (inverse) Fourier transform, the computation of functions of complex number, especially the logarithm of complex number, the ca
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https://doi.org/10.1007/978-0-387-09766-4a based on a stock price process generated by a mixture of a Brownian motion and a Poisson process. This mixed process is also called the jump-diffusion process. The requirement for a jump component in a stock price process is intuitive, and supported by the big crashes in stock markets: The Black M
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https://doi.org/10.1007/978-0-387-09766-4 be regarded as two special cases of Lévy process, and have only finite activity in a finite time interval. In this chapter, we only consider Lévy processes with infinity activity in a finite time interval. With respect to jump event modeling in finance, compound Poisson jumps discussed in Chapter 7
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