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 Asian Option Pricing Under Regime Switching Jump Diffusions and Stochastic Volatility Models written by Justin Kirkby and published by . This book was released on 2020 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with jumps. The method combines Continuous-Time Markov Chain (CTMC) approximation, with Fourier pricing techniques. In particular, our method encompasses Heston, Hull-White, Stein-Stein, 3/2 model as well as recently proposed Jacobi, alpha-Hypergeometric, and 4/2 models, for virtually any type of jump amplitude distribution in the return process. This framework thus provides a unified approach to pricing Asian options in stochastic jump diffusion models and is readily extended to alternative exotic contracts. We also derive a characteristic function recursion by generalizing the Carverhill-Clewlow factorization which enables the application of transform methods in general. Numerical results are provided to illustrate the effectiveness of the method. Various extensions of this method have since been developed, including the pricing of barrier, American, and realized variance derivatives.
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 FFIT 2022 written by Holger Haldenwang and published by European Alliance for Innovation. This book was released on 2023-04-14 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2022 International Conference on Financial Innovation, FinTech and Information Technology (FFIT 2022), hosted by Shenzhen University of Technology and organized by the Financial Innovation and Fintech Research Center of Shenzhen University of Technology, was held on October 28-30, 2022 in Shenzhen, China. Due to the current COVID-19 pandemic and the strict travelling rules, it is still difficult to take international travel for all our attendees to participate in the conference. Therefore, FFIT 2022 was held as a hybrid event. FFIT 2022 brought together innovative academics and industrial experts in the field of Financial Innovation, Financial Technology and Information Technology to discuss the latest research results in this field.
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 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 American Asian Option Pricing Based on Monte Carlo Simulation Method written by Shiguang Han and published by . This book was released on 2012 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient Option Pricing by Frame Duality with the Fast Fourier Transform written by Justin Kirkby and published by . This book was released on 2016 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a method for efficiently inverting analytic characteristic functions using frame projection, as in the case of Heston's model and exponential Levy models. Utilizing the duality theory of Riesz bases, we derive analytical formulas for coefficients of the orthogonally projected density, which are computed numerically with exponential convergence by the FFT. Convergence is demonstrated for geometric Asian options as well as the pricing of baskets of European options. The method is compared to state-of-the-art procedures to demonstrate its efficiency and robustness, without requiring any user-supplied "control parameters." Even greater improvement is observed for the method's extension to arithmetic Asian option pricing, as well as for Bermudan and barrier options, and credit default swaps, which will appear in follow up papers that expand on the foundations developed in this work.
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 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 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 Theory of Continously sampled Asian Option Pricing written by Jin E. Zhang and published by . This book was released on 2000 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simple Fast and Flexible Pricing of Asian Options written by Timothy Klassen and published by . This book was released on 2015 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a modified binomial method that provides a simple and unified framework for the valuation of various kinds of Asian options (American or European, arithmetic or geometric, fixed or floating strike, discrete or continuous sampling and dividends, partial Asians). The Greeks can also be calculated accurately and stably. The method is a refinement of that of Hull and White, where at each node of a standard binomial tree one also considers a table of possible values of the average. To avoid the exponential explosion of the size of this table in the arithmetic average case, one considers a smaller set of representative values for the average, interpolates when necessary, and otherwise uses standard backward recursion to value the option. We present an efficient implementation of this idea. In particular, we insure that option values are smooth as a function of the number of binomial time periods N, so that Richardson extrapolation can be applied to eliminate 1/N (and sometimes higher-order) corrections, dramatically increasing the speed of the method. We provide detailed checks and illustrations, showing that our approach can achieve any desired level of accuracy for convection or diffusion dominated regimes and for long or short maturities. It is typically much faster than standard PDE and Monte Carlo approaches.
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.
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 Double Spiral Method Gamma Transform and Pricing Arithmetic Asian Options written by Sergei Levendorskii and published by . This book was released on 2016 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: A backward induction procedure for pricing arithmetic Asian options in Levy models is realized in the dual space. Each step of the procedure is the composition of a multiplication operators by an explicitly given function, and the convolution operator ${ cal H}_ Ga$, which belongs to a class of natural generalizations of the Hilbert transform ${ cal H}$. The kernel of ${ cal H}_ Ga$ being $(1/2 pi )^{-1} Ga(i( eta- xi))$, we call ${ cal H}_ Ga$ the Gamma transform. An efficient realization of the procedure (Double-Spiral method) is based on calculations of the functions on two parallel lines, using the fast convolution.
