Download or read book An Accurate and Efficient Method for Pricing Asian Options written by Chuang-Chang Chang and published by . This book was released on 2003 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide an accurate and efficient method for valuing Asian options that works well for the low and medium volatility as well as longer average time window. Numerical results show that our method significantly outperforms the other analytic approximation methods in the literature. The pricing errors in terms of mean square errors for calculating a bundle of Asian options are less than one percent. Our method is fast and efficient compared to the Monte Carlo benchmark method adopted as well.
Download or read book Accurate Efficient Pricing of Arithmetic Average Asian Options Within the Hull White Method written by Pratik Ramprasad and published by . This book was released on 2015 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulation or other appro ...
Download or read book An Efficient and Stable Method for Short Maturity Asian Options written by Rupak Chatterjee and published by . This book was released on 2017 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop a Markov chain-based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a closed-form approximation involving only matrices. It is an accurate, efficient, and stable method for the pricing and hedging of short maturity arithmetic Asian options for which previous methods in the literature have shown either slower convergence or instabilities in hedging parameters. We also consider the pricing and hedging of floating-strike Asian options and fixed-strike in-progress Asian options, and demonstrate that our method is as good as and sometimes better than existing approximation methods in the literature.
Download or read book An Efficient Transform Method for Asian Option Pricing written by Justin Kirkby and published by . This book was released on 2016 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper introduces a novel method to price arithmetic Asian options in Levy-driven models, with discrete and continuous averaging, by expanding on the approach of sequential characteristic function recovery. By utilizing frame duality and a FFT-based implementation of density projection, we obtain rapidly converging value approximations to high precision, consistently resulting in a 10- to 100-fold time reduction compared to state-of-the-art procedures. Theoretical convergence rates are confirmed by an in-depth analysis of error propagation. Formulas for Greeks are provided, in addition to generalized averaging and in-progress option pricing.
Download or read book Efficient Pricing of Discrete Arithmetic Asian Options Under Mean Reversion and Jumps Based on Fourier Cosine Expansions written by Chun-Sung Huang and published by . This book was released on 2016 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose an efficient pricing method for arithmetic Asian options based on Fourier-cosine expansions. In particular, we allow for mean reversion and jumps in the underlying price dynamics. There is an extensive body of empirical evidence in the current literature that points to the existence and prominence of such anomalies in the prices of certain asset classes, such as commodities. Our efficient pricing method is derived for the discretely monitored versions of the European-style arithmetic Asian options. The analytical solutions obtained from our Fourier-cosine expansions are compared to the benchmark fast Fourier transform based pricing for the examination of its accuracy and computational efficiency.
Download or read book Valuing American Asian Options with Least Squares Monte Carlo and Low Discrepancy Sequences written by Andries Jacobus Van Niekerk and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: There exists no closed form approximation for arithmetically calculated Asian options, but research has shown that closed form approximations are possible for Geometrically calculated Asian options. The aim of this dissertation is to effectively price American Asian options with the least squares Monte Carlo approach (Longstaff & Schwartz, 2001), applying Low discrepancy sequences and variance reduction techniques. We evaluate how these techniques affect the pricing of American options and American Asian options in terms of accuracy, computational efficiency, and computational time used to implement these techniques. We consider the effect of, Laguerre-, weighted Laguerre-, Hermite-, and Monomial-basis functions on the Longstaff and Schwartz (2001) model. We briefly investigate GPU optimization of the Longstaff and Schwartz algorithm within Matlab. We also graph the associated implied and Local volatility surfaces of the American Asian options to assist in the practical applicability of these options.
Download or read book A General Framework for Pricing Asian Options Under Stochastic Volatility on Parallel Architectures written by Stefania Corsaro and published by . This book was released on 2019 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.
Download or read book Pricing Bounds and Approximations for Discrete Arithmetic Asian Options Under Time Changed L vy Processes written by Pingping Zeng and published by . This book was released on 2015 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive efficient and accurate analytical pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes. By extending the conditioning variable approach, we derive the lower bound on the Asian option price and construct an upper bound based on the sharp lower bound. We also consider the general partially exact and bounded (PEB) approximations, which include the sharp lower bound and partially conditional moments matching approximation as special cases. The PEB approximations are known to lie between a sharp lower bound and an upper bound. Our numerical tests show that the PEB approximations to discrete arithmetic Asian option prices can produce highly accurate approximations when compared to other approximation methods. Our proposed approximation methods can be readily applied to pricing Asian options under the most common types of underlying asset price processes, like the Heston stochastic volatility model nested in time-changed Lévy processes with leverage effect.
Download or read book Efficient Pricing of an Asian Put Option Using Stiff ODE Methods written by and published by . This book was released on 2007 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Financial mathematics is a branch of mathematics that assesses the risk and value of various financial instruments. Banks, companies, and other institutions mitigate their risk through financial instruments known as derivatives, that derive their value from some underlying asset. The equations that arise from pricing and modeling can be very complex, leading to the necessity of numerical methods. This project studied the use of certain numerical methods for the pricing of a particular type of option called an Asian option. Asian options can provide favorable risk profiles because the payout is determined based on the average value over a time period, rather than the final value. The price of an Asian option is governed by a partial differential equation in three variables: stock price, average price over the current time interval, and time. The solution method was first to discretize the partial differential equation into a system of ordinary differential equations. Next, the ODE system was integrated using a stiff-ODE solver available in MATLAB. Enhancements to this solution method include specifying the sparsity pattern, implementing an iterative linear solver (GMRES) in place of MATLAB's built-in direct linear solver, and using preconditioning to improve the solution characteristics of that solver.
Download or read book Bounds for In Progress Floating Strike Asian Options Using Symmetry written by Vicky Henderson and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies symmetries between fixed and floating-strike Asian options and exploits this symmetry to derive an upper bound for the price of a floating-strike Asian. This bound only involves fixed-strike Asians and vanillas, and can be computed simply given one of the many efficient methods for pricing fixed-strike Asian options. The bound coincides with the true price until after the averaging has begun and again at maturity. The bound is compared to benchmark prices obtained via Monte Carlo simulation in numerical examples.
Download or read book Algorithms ESA 2002 written by Rolf Möhring and published by Springer. This book was released on 2003-08-02 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the 74 contributed papers and abstracts of 4 of the 5 invited talks presented at the 10th Annual European Symposium on Algorithms (ESA 2002), held at the University of Rome “La Sapienza”, Rome, Italy, 17-21 September, 2002. For the ?rst time, ESA had two tracks, with separate program committees, which dealt respectively with: – the design and mathematical analysis of algorithms (the “Design and An- ysis” track); – real-world applications, engineering and experimental analysis of algorithms (the “Engineering and Applications” track). Previous ESAs were held in Bad Honnef, Germany (1993); Utrecht, The Neth- lands (1994); Corfu, Greece (1995); Barcelona, Spain (1996); Graz, Austria (1997); Venice, Italy (1998); Prague, Czech Republic (1999); Saarbruc ̈ ken, Ger- ? many (2000), and Arhus, Denmark (2001). The predecessor to the Engineering and Applications track of ESA was the Annual Workshop on Algorithm En- neering (WAE). Previous WAEs were held in Venice, Italy (1997), Saarbruc ̈ ken, ? Germany (1998), London, UK (1999), Saarbru ̈cken, Germany (2000), and Arhus, Denmark (2001). The proceedings of the previous ESAs were published as Springer LNCS volumes 726, 855, 979, 1284, 1461, 1643, 1879, and 2161. The proceedings of WAEs from 1999 onwards were published as Springer LNCS volumes 1668, 1982, and 2161.
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces 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.
Download or read book Numerical Methods for Laplace Transform Inversion written by Alan M. Cohen and published by Springer Science & Business Media. This book was released on 2007-06-16 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations.
Download or read book Research in Finance written by Andrew H. Chen and published by Emerald Group Publishing. This book was released on 2009-02-20 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains topics that include the design of a country's financial safety nets, the effective policies of acquiring failed banks in reducing moral hazard problems, the voluntary disclosure of real options by corporate managers, and the interrelationship between the housing and general economic activities.
Download or read book The Derivatives Sourcebook written by Terence Lim and published by Now Publishers Inc. This book was released on 2006 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Derivatives Sourcebook is a citation study and classification system that organizes the many strands of the derivatives literature and assigns each citation to a category. Over 1800 research articles are collected and organized into a simple web-based searchable database. We have also included the 1997 Nobel lectures of Robert Merton and Myron Scholes as a backdrop to this literature.
Download or read book Pricing of American Style Fixed Strike Asian Options with Continuous Arithmetic Average written by Seung-Young Oh and published by . This book was released on 2004 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article explores the analytic valuation of American-style fixed strike Asian option or average rate option based on the continuous arithmetic average in the Black-Scholes framework. Because there is no closed-form exact valuation formula for the average rate option with the arithmetic average, a very well-approximated arithmetic average density function is used for the valuation. The optimal exercise boundary and the values of American average rate options are compared with those of American plain vanilla options. Especially, this article shows that American average rate option can have two different optimal exercise boundaries depending on the parameters. Numerical experiments are also performed to demonstrate the influence of the component factors on the values of American average rate options and to illustrate the accuracy and efficiency of the valuation formula.
Download or read book Algorithmic Applications in Management written by Nimrod Megiddo and published by Springer. This book was released on 2005-05-24 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume were presented at the 1st International Conference on Algorithmic Applications in Management (AAIM 2005), held June 22 –25, 2005 in Xian, China.
