Download Free Option Pricing Models Built From Levy Processes Book in PDF and EPUB Free Download. You can read online Option Pricing Models Built From Levy Processes and write the review.

This thesis seeks to studying two different methods of option pricing - one introduced in Carr and Madan (1999), and the other one in F.Fang and Oosterlee (2008) - suitable for stock prices following stochastic processes whose characteristic function is known. The advantage of these methods is that they do not require an explicit formula for the density function. For each method, we determine good computation parameters before comparing them in terms of efficiency and accuracy. As an intermediary step, and because the Carr-Madan method is not compatible with a customised strike grid, we study two interpolation methods : the linear and the natural cubic spline interpolations. We also discuss the calibration problem, explain why it is not as straightforward as it may seem, and compare the results obtained for both models.
This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric L(r)vy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problem
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
We analyze the specifications of option pricing models based on time-changed Levy processes. We classify option pricing models based on the sucture of the jump component in the underlying return process, the source of stochastic volatility, and the specification of the volatility process itself. Our estimation of a variety of model specifications indicates that to better capture the behavior of the Samp;P 500 index options, we must incorporate a high frequency jump component in the return process and generate stochastic volatilities from two different sources, the jump component and the diffusion component.
We apply stochastic time change to Levy processes to generate a wide variety of tractable option pricing models. In particular, we prove a fundamental theorem that transforms the characteristic function of the time-changed Levy process into the Laplace transform of the stochastic time under appropriate measure change. We extend the traditional measure theory into the complex domain and define the measure change by a class of complex valued exponential martingales. We provide extensive examples to illustrate its applications and its link to existing models in the literature.
Financial mathematics has recently enjoyed considerable interest on account of its impact on the finance industry. In parallel, the theory of L?vy processes has also seen many exciting developments. These powerful modelling tools allow the user to model more complex phenomena, and are commonly applied to problems in finance. L?vy Processes in Finance: Pricing Financial Derivatives takes a practical approach to describing the theory of L?vy-based models, and features many examples of how they may be used to solve problems in finance. * Provides an introduction to the use of L?vy processes in finance. * Features many examples using real market data, with emphasis on the pricing of financial derivatives. * Covers a number of key topics, including option pricing, Monte Carlo simulations, stochastic volatility, exotic options and interest rate modelling. * Includes many figures to illustrate the theory and examples discussed. * Avoids unnecessary mathematical formalities. The book is primarily aimed at researchers and postgraduate students of mathematical finance, economics and finance. The range of examples ensures the book will make a valuable reference source for practitioners from the finance industry including risk managers and financial product developers.
There are a number of recent models that extend the Black and Scholes (1973) model by considering stochastic volatility and/or jumps, and appear to show good empirical performance. In this paper we consider some of the most successful models, all of them belonging to the class of Levy processes, and further study their empirical performance; in particular we consider their pricing performance for American options and their performance in terms of their put-call robustness; we find that their performance is good on the call side, but their put-call robustness gets lower scores than Black and Scholes (1973) with the possible exception of Carr, Geman, Madan and Yor (2002); we interpret our results as evidence of overfitting.
From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
A model is developed that can price path dependent options when the underlying process is an exponential Levy process with closed form conditional characteristic function. The model is an extension of a recent quadrature option pricing model so that it can be applied with the use of Fourier and Fast Fourier transforms. Thus the model possesses nice features of both transform and quadrature option pricing techniques since it can be applied for a very general set of underlying Levy processes and can handle exotic path dependent features. The model is applied to European and Bermudan options for geometric Brownian motion, a jump-diffusion process, a variance gamma process and a normal inverse Gaussian process. However it must be noted that the model can also price other path dependent exotic options such as lookback and Asian options.
ABSTRACT: This dissertation is concerned with the pricing of path-dependent options where the underlying asset is modeled as a continuous-time exponential Lévy process and is monitored at discrete dates. These options enable their users to tailor random payoff outcomes to their particular risk profiles and are widely used by hedgers such as large multinational corporations and speculators alike. The use of continuous-time models since the breakthrough paper of Black and Scholes has been greatly facilitated by advances in stochastic calculus and the mathematical elegance it provides. The recent financial crisis started in 2008 has highlighted the importance of models that incorporate the possibility of sudden, large jumps as well as the higher likelihood of adverse outcomes as compared with the classical Black-Scholes model. Increasingly, exponential Lévy processes have become preferred alternatives, thanks in particular to the explicit Lévy-Khinchin representation of their characteristic functions. On the other hand, the restriction of monitoring dates to a discrete set increases the mathematical and computational complexity for the pricing of path-dependent options even in the classical Black-Scholes model. This dissertation develops new techniques based on recent advances in the fast evaluation and inversion of Fourier and Hilbert transforms as well as classical results in fluctuation theory, particularly those involving random walk duality and ladder epochs.