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by Ole E. Barndorff-Nielsen and Neil Shephard
In this article we provide a brief review of part of the literature on this topic, focusing on high frequency ex-post measures of volatility and models of volatility driven by L
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Hans Buehler
Contents

Some examples

Levy processes

Using Levy processes to model the stock price process

Numerical methods

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This article introduces a method for building analytically tractable option pricing models that combine state-dependent volatility, stochastic volatility and jumps. The eigenfunction expansion method is used to add jumps and stochastic volatility to hypergeometric Brownian motions. Claudio Albanese and Alexey Kuznetsov conclude that such comprehensive unified models are not only able to reflect the complexities of exotic option prices, but are also analytically tractable

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Wim Schoutens
Abstract
In this paper we overview the pricing of several so-called exotic options in the nowdays quite popular exponential Levy models.
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Yoshio Miyahara
Nagoya City University

Alexander Novikov
University of Technology
Sydney

Abstract We consider models for stock prices which relates to random processes with independent homogeneous increments Levy processes These models are arbitrage free but correspond to the incomplete financial market There are many dierent approaches for pricing of nancial derivatives We consider here mainly the approach which is based on minimal relative entropy This method is related to an utility function of exponential type and the Esscher transformation of probabilistic measures

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Abstract As is well known, the classic Black-Scholes option pricing model assumes that returns follow Brownian motion. It is widely recognized that return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. We propose that time-changed L
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Peter Carr
Bloomberg LP and Courant Institute, NYU
Liuren Wu
Zicklin School of Business, Baruch College

Overview
Apply stochastic time change to L
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Abstract:
In this paper, we assume that log returns can be modelled by a Levy process. We give explicit formulae for option prices by means of the Fourier transform. We explain how to infer the characteristics of the Levy process from option prices.
This enables us to generate an implicit volatility surface implied by market data. This model is of particular interest since it extends the seminal Black Scholes [1973] model consistently with volatility smile.


Keywords: Levy process, Fourier and Laplace transform, Smile

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