Download or read book Numerical Techniques for the Valuation of Asian Options and Double barrier Options written by Tong Wang and published by . This book was released on 1997 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Pricing of Double Barrier Options and Their Variations written by Anlong Li and published by . This book was released on 2006 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives closed-form solutions for double barrier options under the usual assumptions of the Black-Scholes (1973) model using reflection principle in Brownian motions. While we recover the well-known valuation formulae for standard double barrier options, we show how to apply the same technique to variations of double barrier options. The option payoff function we use is the simplest one that includes call, put, and digital options as special cases. The solution is expressed in general as summations of an infinite number of normal distribution functions for standard double barrier options and in many non-trivial cases the solution consists of only finite terms. Double barrier options with rebates and exponentially curved barriers are also considered. Numerical approximations are provided as a verification of the closed-form solutions.
Download or read book American Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-12-17 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
Download or read book The Valuation of American Barrier Options Using the Decomposition Technique written by Marti G. Subrahmanyam and published by . This book was released on 2008 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose an alternative approach for pricing and hedging non-standard American options. In principle, the proposed approach applies to any kind of American-style contract for which the payoff function has a Markovian representation in the state space. Specifically, we obtain an analytic solution for the value and hedge parameters of barrier options, an important example of path-dependent options. The solution includes standard American options as a special case. The analytic formula also allows us to identify and exploit two key properties of the optimal exercise boundary - homogeneity in price parameters and time-invariance - for American options. In addition, some new put-call ``symmetryquot; relations are also derived. These properties suggest a new, efficient and integrated approach to pricing and hedging a variety of standard and non-standard American options. From an implementation perspective, this approach avoids the current practice of repetitive computation of option prices and hedge ratios. Our implementation of the analytic formula for barrier options indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. In some cases, our method is substantially faster than existing numerical methods with equal accuracy. In particular, the method overcomes the difficulty that existing numerical methods have in dealing with prices close to the barrier, the case where the barrier matters most.
Download or read book Numerical Methods in Computational Finance written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2022-03-21 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a detailed and step-by-step introduction to the mathematical foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. The book is structured so that it can be read by beginners, novices and expert users. Part A Mathematical Foundation for One-Factor Problems Chapters 1 to 7 introduce the mathematical and numerical analysis concepts that are needed to understand the finite difference method and its application to computational finance. Part B Mathematical Foundation for Two-Factor Problems Chapters 8 to 13 discuss a number of rigorous mathematical techniques relating to elliptic and parabolic partial differential equations in two space variables. In particular, we develop strategies to preprocess and modify a PDE before we approximate it by the finite difference method, thus avoiding ad-hoc and heuristic tricks. Part C The Foundations of the Finite Difference Method (FDM) Chapters 14 to 17 introduce the mathematical background to the finite difference method for initial boundary value problems for parabolic PDEs. It encapsulates all the background information to construct stable and accurate finite difference schemes. Part D Advanced Finite Difference Schemes for Two-Factor Problems Chapters 18 to 22 introduce a number of modern finite difference methods to approximate the solution of two factor partial differential equations. This is the only book we know of that discusses these methods in any detail. Part E Test Cases in Computational Finance Chapters 23 to 26 are concerned with applications based on previous chapters. We discuss finite difference schemes for a wide range of one-factor and two-factor problems. This book is suitable as an entry-level introduction as well as a detailed treatment of modern methods as used by industry quants and MSc/MFE students in finance. The topics have applications to numerical analysis, science and engineering. More on computational finance and the author’s online courses, see www.datasim.nl.
Download or read book Pricing Asian Options written by Akos Horvath and published by . This book was released on 2016 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The derivation of Asian option value has posed a challenge to financial mathematicians for the last two decades. Fu, Madan and Wang (1999) made a comparison between the Laplace transform approach and the Monte Carlo approach, and found that the numerical inversion method encountered severe numerical instabilities when volatility was low or maturity was short.In this paper, we seek to answer the question whether it is possible to improve on the efficiency of the inversion, implementing and comparing different numerical algorithms, so that the Laplace transform could be used in real-life situations. We also look into whether today's superior computer environment has changed the relative strength of numerical and simulation approaches with regards to Asian option pricing.Based on an detailed comparison of methods, we find that the speed and reliability of the Laplace transform inversion could be further enhanced, pushing down the prior critical value from 0.01 to 0.005 and calculation time from 20-30 seconds to 3-4 seconds. Also, as a conclusion of our research we suggest that the simulation approach be used when sigma^2*T
Download or read book An Introduction to Financial Option Valuation written by Desmond J. Higham and published by Cambridge University Press. This book was released on 2004-04-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.
Download or read book Mathematical Models of Financial Derivatives written by Yue-Kuen Kwok and published by Springer Science & Business Media. This book was released on 2008-07-10 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.
Download or read book Advanced Numerical Methods in Applied Sciences written by Luigi Brugnano and published by MDPI. This book was released on 2019-06-20 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
Download or read book Pricing Barrier Options with Numerical Methods written by Candice Natasha De Ponte and published by . This book was released on 2013 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pricing Barrier Options with Numerical Methods written by Candice Natasha De Ponte and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Barrier options -- Black-Scholes -- Binomial method -- Trinomial method -- Monte Carlo simulation -- Finite difference method.
Download or read book A Complete Analytical Solution of the Asian Option Pricing Within the Heston Model for Stochastic Volatility written by Alexander Izmailov and published by . This book was released on 2015 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first ever explicit formulation of the concept of the option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True Value-at-Risk and Option Based Hedging Strategies” and “Complete Analytical Solution of the Asian Option Pricing and Asian Option Value-at-Risk Problems. A Probability Density Function Approach.” See links: 'http://ssrn.com/abstract=2489601' http://ssrn.com/abstract=2489601 and 'http://ssrn.com/abstract=2546430' http://ssrn.com/abstract=2546430.The first ever explicit formulation of the concept of the options' probability density functions within the framework of stochastic volatility (Heston model) has been introduced in our publications “Complete Analytical Solution of the Heston Model for Option Pricing and Value-at-Risk Problems: A Probability Density Function Approach”, “Complete Analytical Solution of the American Style Option Pricing with Constant and Stochastic Volatilities: A Probability Density Function Approach” and “A Complete Analytical Resolution of the Double Barrier Option's Pricing Within the Heston Model. A Probability Density Approach.” See links:'http://ssrn.com /abstract=2549033' http://ssrn.com/abstract=2549033 and 'http://ssrn.com/abstract=2554038' http://ssrn.com/abstract=2554038 and 'http://ssrn.com/abstract=2605948' http://ssrn.com/abstract=2605948.In this paper we report complete analytical closed-form results for the European style Asian Options considered within the Heston model for Stochastic Volatility (SV). Our discovery of the probability density function of the European style Asian Options with SV enables exact closed-form representation of its expected value (price) for the first time ever. Our formulation of the probability density function for the European style Asian Options with SV is expressive enough to enable derivation for the first time ever of corollary analytical closed-form results for such Value-At-Risk characteristics as the probabilities that an Asian Option with SV will be below or above any threshold at any future time before or at termination. Such assessments are absolutely out of reach of the current published methods for treating Asian Options even in the framework of constant volatility.All numerical evaluations based on our analytical results are practically instantaneous and absolutely accurate.
Download or read book Valuation Empirical Analysis and Optimal Exercise of Open End Turbo Certificates written by Sebastian Paik and published by University of Bamberg Press. This book was released on 2014 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Valuation of American Barrier Options Using The Decomposition Technique written by Bin Gao and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call quot;symmetryquot; relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options. Our implementation of the obtained solution indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and efficiency. In particular, the method is free of the difficulty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.
Download or read book Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility written by Oliver Faulhaber and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book FX Options and Structured Products written by Uwe Wystup and published by John Wiley & Sons. This book was released on 2017-06-30 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Guidance to Excelling in the FX Market Once you have a textbook understanding of money market and foreign exchange products, turn to FX Options and Structured Products, Second Edition, for the beyond-vanilla options strategies and traded deals proven superior in today’s post-credit crisis trading environment. With the thoroughness and balance of theory and practice only Uwe Wystup can deliver, this fully revised edition offers authoritative solutions for the real world in an easy-to-access format. See how specific products actually work through detailed case studies featuring clear examples of FX options, common structures and custom solutions. This complete resource is both a wellspring of ideas and a hands-on guide to structuring and executing your own strategies. Distinguish yourself with a valued skillset by: Working through practical and thought-provoking challenges in more than six dozen exercises, all with complete solutions in a companion volume Gaining a working knowledge of the latest, most popular products, including accumulators, kikos, target forwards and more Getting close to the everyday realities of the FX derivatives market through new, illuminating case studies for corporates, municipalities and private banking FX Options and Structured Products, Second Edition is your go-to road map to the exotic options in FX derivatives.
Download or read book Numerical Methods and Applications written by Geno Nikolov and published by Springer. This book was released on 2019-01-21 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-conference proceedings of the 9th International Conference on Numerical Methods and Applications, NMA 2018, held in Borovets, Bulgaria, in August 2018. The 56 revised regular papers presented were carefully reviewed and selected from 61 submissions for inclusion in this book. The papers are organized in the following topical sections: numerical search and optimization; problem-driven numerical method: motivation and application, numerical methods for fractional diffusion problems; orthogonal polynomials and numerical quadratures; and Monte Carlo and Quasi-Monte Carlo methods.
