Semi Analytical Valuation For Discrete Barrier Options Under Time Dependent Levy Processes

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Semi-Analytical Valuation for Discrete Barrier Options Under Time-Dependent Lévy Processes

Author : Guanghua Lian
Publisher :
ISBN 13 :
Total Pages : 51 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Semi-Analytical Valuation for Discrete Barrier Options Under Time-Dependent Lévy Processes by : Guanghua Lian

Download or read book Semi-Analytical Valuation for Discrete Barrier Options Under Time-Dependent Lévy Processes written by Guanghua Lian and published by . This book was released on 2017 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple analytical solutions for the prices of discretely monitored barrier options do not yet exist in the literature. This paper presents a semi-analytical and fully explicit solution for pricing discretely monitored barrier options when the underlying asset is driven by a general Lévy process. The explicit formula only involves elementary functions, and the Greeks are also explicitly available with little additional computation. By performing a Z-transform, we reduce the valuation problem to an integral equation. This equation is solved analytically with the solution expressed in terms of a Fourier cosine series. We then manage to analytically carry out the Z-transform inversion, and obtain a semi-analytical formula for pricing discrete barrier options. We establish the theoretical error bound and analyze the convergence order of our method. Numerical implementation demonstrates that our numerical results are accurate and efficient, and match up with the results from the benchmark methods in the literature.

Pricing Path-Dependent Options with Discrete Monitoring Under Time-Changed Levy Processes

Author : Yuji Umezawa
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (13 download)

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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.

On the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model

Author : Susanne Griebsch
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis On the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model by : Susanne Griebsch

Download or read book On the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model written by Susanne Griebsch and published by . This book was released on 2010 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We focus on closed-form option pricing in Heston's stochastic volatility model, where closed-form formulas exist only for a few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this closed-form approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times.

Pricing Discretely Monitored Barrier Options and Defaultable Bonds in Levy Process Models

Author : Liming Feng
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Pricing Discretely Monitored Barrier Options and Defaultable Bonds in Levy Process Models by : Liming Feng

Download or read book Pricing Discretely Monitored Barrier Options and Defaultable Bonds in Levy Process Models written by Liming Feng and published by . This book was released on 2010 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a novel method to price discretely-monitored single- and double-barrier options in Levy process-based models. The method involves a sequential evaluation of Hilbert transforms of the product of the Fourier transform of the value function at the previous barrier monitoring date and the characteristic function of the (Esscher transformed) Levy process. A discrete approximation with exponentially decaying errors is developed based on the Whittaker cardinal series (Sinc expansion) in Hardy spaces of functions analytic in a strip. An efficient computational algorithm is developed based on the fast Hilbert transform that, in turn, relies on the FFT-based Toeplitz matrix-vector multiplication. Our method also provides a natural framework for credit risk applications, where the firm value follows an exponential Levy process and default occurs at the first time the firm value is below the default barrier on one of a discrete set of monitoring dates.

Valuing Time-Dependent CEV Barrier Options

Author : Chi-Fai Lo
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Valuing Time-Dependent CEV Barrier Options by : Chi-Fai Lo

Download or read book Valuing Time-Dependent CEV Barrier Options written by Chi-Fai Lo and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we have derived the analytical kernels of the pricing formulae of the CEV knockout options with time-dependent parameters for a parametric class of moving barriers. By a series of similarity transformations and changing variables, we are able to reduce the pricing equation to one which is reducible to the Bessel equation with constant parameters. These results enable us to develop a simple and efficient method for computing accurate estimates of the CEV single-barrier option prices as well as their upper and lower bounds when the model parameters are time-dependent. By means of the multi-stage approximation scheme, the upper and lower bounds for the exact barrier option prices can be efficiently improved in a systematic manner. It is also natural that this new approach can be easily applied to capture the valuation of other standard CEV options with specified moving knockout barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, more comparative pricing and precise risk management in equity options can be achieved by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

Lie Algebraic Approach for Pricing Moving Barrier Options with Time-Dependent Parameters

Author : Chi-Fai Lo
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Lie Algebraic Approach for Pricing Moving Barrier Options with Time-Dependent Parameters by : Chi-Fai Lo

Download or read book Lie Algebraic Approach for Pricing Moving Barrier Options with Time-Dependent Parameters written by Chi-Fai Lo and published by . This book was released on 2007 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers.In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.

Pricing Forward Start Options in Models Based on (Time-Changed) Levy Processes

Author : Philipp Beyer
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Pricing Forward Start Options in Models Based on (Time-Changed) Levy Processes by : Philipp Beyer

Download or read book Pricing Forward Start Options in Models Based on (Time-Changed) Levy Processes written by Philipp Beyer and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Options depending on the forward skew are very popular. One such option is the forward starting call option - the basic building block of a cliquet option. Widely applied models to account for the forward skew dynamics to price such options include the Heston model, the Heston-Hull-White model and the Bates model. Within these models solutions for options including forward start features are available using (semi) analytical formulas. Today exponential (subordinated) Levy models being increasingly popular for modelling the asset dynamics. While the simple exponential Levy models imply the same forward volatily surface for all future times the subordinated models do not. Depending on the subordinator the dynamic of the forward volatility surface and therefore stochastic volatility can be modelled. Analytical pricing formulas based on the characteristic function and Fourier transform methods are available for the class of these models. We extend the applicability of analytical pricing to options including forward start features. To this end we derive the forward characteristic functions which can be used in Fourier transform based methods. As examples we consider the Variance Gamma model and the NIG model subordinated by a Gamma Ornstein Uhlenbeck process and respectively by an Cox-Ingersoll-Ross process. We check our analytical results by applying Monte Carlo methods. These results can for instance be applied to calibration of the forward volatility surface.

Economic Dynamics

Author : Chester W. Hurlington
Publisher :
ISBN 13 :
Total Pages : 236 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis Economic Dynamics by : Chester W. Hurlington

Download or read book Economic Dynamics written by Chester W. Hurlington and published by . This book was released on 2009 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic dynamic theory includes dynamic games, dynamic general equilibrium theory, and empirical studies. The following topics are subsumed: business cycles, asset pricing, search models, intergenerational issues, fertility, financial systems. This book presents the latest research from around the globe.

Valuing Double Barrier Options With Time-Dependent Parameters by Fourier Series Expansion

Author : Chi-Fai Lo
Publisher :
ISBN 13 :
Total Pages : 5 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Valuing Double Barrier Options With Time-Dependent Parameters by Fourier Series Expansion by : Chi-Fai Lo

Download or read book Valuing Double Barrier Options With Time-Dependent Parameters by Fourier Series Expansion written by Chi-Fai Lo and published by . This book was released on 2007 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based upon the Fourier series expansion, we propose a simple and easy-to-use approach for computing accurate estimates of Black-Scholes double barrier option prices with time-dependent parameters. This new approach is also able to provide tight upper and lower bounds of the exact barrier option prices. Furthermore, this approach can be straightforwardly extended to the valuation of standard European options with specified moving boundaries as well.

Path-dependent Option Pricing

Author : Gudbjort Gylfadottir
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (76 download)

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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.

Efficient Evaluation of Double-Barrier Options and Joint CPDF of a Levy Process and Its Two Extrema

Author : Svetlana Boyarchenko
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis Efficient Evaluation of Double-Barrier Options and Joint CPDF of a Levy Process and Its Two Extrema by : Svetlana Boyarchenko

Download or read book Efficient Evaluation of Double-Barrier Options and Joint CPDF of a Levy Process and Its Two Extrema written by Svetlana Boyarchenko and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Levy models; the calculations are in the dual space, and the Wiener-Hopf factorization is used. For wide regions in the parameter space, the precision of the order of 10-15 is achievable in seconds, and of the order of $10-9-10-8 - in fractions of a second. The Wiener-Hopf factors and repeated integrals in the pricing formulas are calculated using sinh-deformations of the lines of integration, the corresponding changes of variables and the simplified trapezoid rule. If the Bromwich integral is calculated using the Gaver-Wynn Rho acceleration instead of the sinh-acceleration, the CPU time is typically smaller but the precision is of the order of 10-9-10-6, at best. Explicit pricing algorithms and numerical examples are for no-touch options, digitals (equivalently, for the joint distribution function of a Levy process and its supremum and infimum processes), and call options. Several graphs are produced to explain fundamental difficulties for accurate pricing of barrier options using time discretization and interpolation-based calculations in the state space.

Analytical Approach to Value Options with State Variables of a Levy System

Author : Thanh Long Nguyen
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Analytical Approach to Value Options with State Variables of a Levy System by : Thanh Long Nguyen

Download or read book Analytical Approach to Value Options with State Variables of a Levy System written by Thanh Long Nguyen and published by . This book was released on 2003 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we present an analytical method in pricing European contingent assets, whose state variables follow a multi-dimensional Levy process. We give an explicit formula for the hypothetical European quot;two-pricequot; call option price by means of the conditional characteristic transform. The work not only unifies and extends the option pricing literature, which focuses on the use of the characteristic function, but also provides the way to formalize and and unify the valuation of the option price, the valuation of the discount bond price, the valuation of the scaled-forward price, and the valuation of the pricing measure in incomplete markets.

Modern Methods in Operator Theory and Harmonic Analysis

Author : Alexey Karapetyants
Publisher : Springer Nature
ISBN 13 : 3030267482
Total Pages : 475 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modern Methods in Operator Theory and Harmonic Analysis by : Alexey Karapetyants

Download or read book Modern Methods in Operator Theory and Harmonic Analysis written by Alexey Karapetyants and published by Springer Nature. This book was released on 2019-08-28 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.

The Complete Guide to Option Pricing Formulas

Author : Espen Gaarder Haug
Publisher : Professional Finance & Investment
ISBN 13 :
Total Pages : 586 pages
Book Rating : 4.3/5 ( download)

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Book Synopsis The Complete Guide to Option Pricing Formulas by : Espen Gaarder Haug

Download or read book The Complete Guide to Option Pricing Formulas written by Espen Gaarder Haug and published by Professional Finance & Investment. This book was released on 2007-01-08 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM contains ... "all pricing formulas, with VBA code and ready-to-use Excel spreadsheets and 3D charts for Greeks (or Option Sensitivities)."--Jacket.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Modern SABR Analytics

Author : Alexandre Antonov
Publisher : Springer
ISBN 13 : 9783030106553
Total Pages : 127 pages
Book Rating : 4.1/5 (65 download)

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Book Synopsis Modern SABR Analytics by : Alexandre Antonov

Download or read book Modern SABR Analytics written by Alexandre Antonov and published by Springer. This book was released on 2019-05-02 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on recent advances in option pricing under the SABR model, this book shows how to price options under this model in an arbitrage-free, theoretically consistent manner. It extends SABR to a negative rates environment, and shows how to generalize it to a similar model with additional degrees of freedom, allowing simultaneous model calibration to swaptions and CMSs. Since the SABR model is used on practically every trading floor to construct interest rate options volatility cubes in an arbitrage-free manner, a careful treatment of it is extremely important. The book will be of interest to experienced industry practitioners, as well as to students and professors in academia. Aimed mainly at financial industry practitioners (for example quants and former physicists) this book will also be interesting to mathematicians who seek intuition in the mathematical finance.

Non-Gaussian Merton-Black-Scholes Theory

Author : Svetlana I. Boyarchenko
Publisher : World Scientific
ISBN 13 : 9810249446
Total Pages : 421 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Non-Gaussian Merton-Black-Scholes Theory by : Svetlana I. Boyarchenko

Download or read book Non-Gaussian Merton-Black-Scholes Theory written by Svetlana I. Boyarchenko and published by World Scientific. This book was released on 2002 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lvy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.