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Path Dependant Option Pricing Under Levy Processes
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Book Synopsis Path Dependant Option Pricing Under Levy Processes by : Conall O'Sullivan
Download or read book Path Dependant Option Pricing Under Levy Processes written by Conall O'Sullivan and published by . This book was released on 2005 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Path-dependent Option Pricing by : Gudbjort Gylfadottir
Download or read book Path-dependent Option Pricing written by Gudbjort Gylfadottir and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Pricing Path-Dependent Options with Discrete Monitoring Under Time-Changed Levy Processes by : Yuji Umezawa
Download or read book Pricing Path-Dependent Options with Discrete Monitoring Under Time-Changed Levy Processes written by Yuji Umezawa and published by . This book was released on 2014 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a pricing method for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a time-changed Levy process. The key to our method is to derive a backward recurrence relation for computing the multivariate characteristic functions of the intertemporal joint distribution of time-changed Levy processes. Using the derived representation of the characteristic function we obtain semi-analytical pricing formulas for geometric Asian, forward start, barrier, fader, and lookback options, all of which are discretely monitored.
Book Synopsis Option Pricing in Incomplete Markets by : Yoshio Miyahara
Download or read book Option Pricing in Incomplete Markets written by Yoshio Miyahara and published by World Scientific. This book was released on 2012 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Lvy 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 problems.
Book Synopsis Option Pricing Under Levy Processes: a Unifying Formula by : Rossella Agliardi
Download or read book Option Pricing Under Levy Processes: a Unifying Formula written by Rossella Agliardi and published by . This book was released on 2009 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing in Some Non-Levy Jump Models by : Lingfei Li
Download or read book Option Pricing in Some Non-Levy Jump Models written by Lingfei Li and published by . This book was released on 2016 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers pricing European options in a large class of one-dimensional Markovian jump processes known as subordinate diffusions, which are obtained by time changing a diffusion process with an independent Levy or additive random clock. These jump processes are non-Levy in general, and they can be viewed as natural generalization of many popular Levy processes used in finance. Subordinate diffusions other richer jump behavior than Levy processes and they have found a variety of applications in financial modelling. The pricing problem for these processes presents unique challenges as existing numerical PIDE schemes fail to be efficient and the applicability of transform methods to many subordinate diffusions is unclear. We develop a novel method based on finite difference approximation of spatial derivatives and matrix eigendecomposition, and it can deal with diffusions that exhibit various types of boundary behavior. Since financial payoffs are typically not smooth, we apply a smoothing technique and use extrapolation to speed up convergence. We provide convergence and error analysis and perform various numerical experiments to show the proposed method is fast and accurate. Extension to pricing path-dependent options will be investigated in a follow-up paper.
Book Synopsis Preference-free Option Pricing with Path-dependent Volatility by : Steven L. Heston
Download or read book Preference-free Option Pricing with Path-dependent Volatility written by Steven L. Heston and published by . This book was released on 1998 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing in a Lévy Process Setting by : Jasper Valstar
Download or read book Option Pricing in a Lévy Process Setting written by Jasper Valstar and published by . This book was released on 2008 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Time-Changed Levy Process and Option Pricing by : Peter Carr
Download or read book Time-Changed Levy Process and Option Pricing written by Peter Carr and published by . This book was released on 2001 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computational Option Pricing Under Jump Diffusion and Lévy Processes by : Eleftheria Chatzipanagou
Download or read book Computational Option Pricing Under Jump Diffusion and Lévy Processes written by Eleftheria Chatzipanagou and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Efficient Option Pricing Under Levy Processes, with CVA and FVA. by : Justin Shek
Download or read book Efficient Option Pricing Under Levy Processes, with CVA and FVA. written by Justin Shek and published by . This book was released on 2015 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We generalize the Piterbarg (2010) model to include 1) bilateral default risk as in Burgard and Kjaer (2012), and 2) jumps in the dynamics of the underlying asset using general classes of Lévy processes of exponential type. We develop an efficient explicit-implicit scheme for European options and barrier options taking CVA-FVA into account. We highlight the importance of this work in the context of trading, pricing and management a derivative portfolio given the trajectory of regulations.
Book Synopsis Hedging for Option Pricing with Regular Levy Processes of Exponential Type by : Yu Dan
Download or read book Hedging for Option Pricing with Regular Levy Processes of Exponential Type written by Yu Dan and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing with Levy Process by : Eric Benhamou
Download or read book Option Pricing with Levy Process written by Eric Benhamou and published by . This book was released on 2001 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes by : Jing-Zhi Huang
Download or read book Specification Analysis of Option Pricing Models Based on Time-Changed Levy Processes written by Jing-Zhi Huang and published by . This book was released on 2003 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze the specifications of option pricing models based on time-changed Levy processes. We classify option pricing models based on the structure 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.
Book Synopsis Exotic Option Pricing and Advanced Lévy Models by : Andreas Kyprianou
Download or read book Exotic Option Pricing and Advanced Lévy Models written by Andreas Kyprianou and published by John Wiley & Sons. This book was released on 2006-06-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Option Pricing Using Lévy Processes by :
Download or read book Option Pricing Using Lévy Processes written by and published by . This book was released on 2007 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pricing of Discretely Sampled Asian Options Under Levy Processes by : Jiayao Xie
Download or read book Pricing of Discretely Sampled Asian Options Under Levy Processes written by Jiayao Xie and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT. We develop a new method for pricing options on discretely sampled arithmetic average in exponential Levy models. The main idea is the reduction to a backward in- duction procedure for the difference Wn between the Asian option with averaging over n sampling periods and the price of the European option with maturity one period. This al- lows for an efficient truncation of the state space. At each step of backward induction, Wn is calculated accurately and fast using a piece-wise interpolation or splines, fast convolu- tion and either flat iFT and (refined) iFFT or the parabolic iFT. Numerical results demonstrate the advantages of the method. Keywords: Option pricing, flat iFT method, parabolic iFT method, FFT, refined and enhanced FFT, Levy processes, KoBoL, CGMY, BM, Asian options.
