Pricing Of Geometric Asian Options In General Affine Stochastic Volatility Models
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Author | : Johannes Ruppert |
Publisher | : |
Total Pages | : 76 |
Release | : 2016 |
Genre | : |
ISBN | : |
"In this thesis, we look at the general affine pricing model introduced in [11]. This model allows to price geometric Asian options, which are of big interest due to their lower volatility in comparison to, for example, European options. Because of their structure and in order to be able to price these options, we look at the basic theory of Lévy processes and stochastic calculus. Furthermore, we provide the detailed description of the parameters of the pricing formulas for some popular specific single-factor stochastic volatility models with jumps and generalize the approach of [11] to multi-factor models"--Abstract, page iii.
Author | : Stefania Corsaro |
Publisher | : |
Total Pages | : 30 |
Release | : 2019 |
Genre | : |
ISBN | : |
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.
Author | : Lu Tian |
Publisher | : |
Total Pages | : 17 |
Release | : 2012 |
Genre | : |
ISBN | : |
Author | : Justin Kirkby |
Publisher | : |
Total Pages | : 39 |
Release | : 2020 |
Genre | : |
ISBN | : |
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.
Author | : José Da Fonseca |
Publisher | : |
Total Pages | : 26 |
Release | : 2015 |
Genre | : |
ISBN | : |
We price for different affine stochastic volatility models some derivatives that recently appeared in the market. These products are characterised by payoffs depending on both stock and its volatility. Using a Fourier-analysis approach, we recover in a much simpler way some results already established in the literature for the single factor specification of the volatility and we push forward our methodology, which turns out to be independent of the dimension of the problem, thanks to a simple conditioning with respect to the subfiltration generated by the variance path. For each product we provide a closed form solution based on the Fast Fourier Transform and we illustrate the results for realistic model parameter values. Also, our results highlight the great flexibility and tractability of the Wishart based stochastic volatility models.
Author | : Yannick Dillschneider |
Publisher | : |
Total Pages | : 12 |
Release | : 2019 |
Genre | : |
ISBN | : |
In this paper, we derive explicit expressions for certain joint moments of stock prices and option prices within a generic affine stochastic volatility model. Evaluation of each moment requires weighted inverse Fourier transformation of a function that is determined by the risk-neutral and real-world characteristic functions of the state vector. Explicit availability of such moment expressions allows to devise a novel GMM approach to jointly estimate real-world and risk-neutral parameters of affine stochastic volatility models using observed individual option prices. Moreover, the moment expressions may be used to include option price information into other existing moment-based estimation approaches.
Author | : Ying Lok Cheung |
Publisher | : |
Total Pages | : 104 |
Release | : 2004 |
Genre | : Options (Finance) |
ISBN | : |
Author | : Mario J. Miranda |
Publisher | : MIT Press |
Total Pages | : 529 |
Release | : 2004-08-20 |
Genre | : Business & Economics |
ISBN | : 0262291754 |
This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on problems in agricultural and resource economics, macroeconomics, and finance. The book also provides an extensive Web-site library of computer utilities and demonstration programs. The book is divided into two parts. The first part develops basic numerical methods, including linear and nonlinear equation methods, complementarity methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. The second part presents methods for solving dynamic stochastic models in economics and finance, including dynamic programming, rational expectations, and arbitrage pricing models in discrete and continuous time. The book uses MATLAB to illustrate the algorithms and includes a utilities toolbox to help readers develop their own computational economics applications.
Author | : Damiaan Lemmens |
Publisher | : |
Total Pages | : 126 |
Release | : 2011 |
Genre | : |
ISBN | : |
Author | : Antoine Petrus Cornelius van der Ploeg |
Publisher | : Rozenberg Publishers |
Total Pages | : 358 |
Release | : 2006 |
Genre | : |
ISBN | : 9051705778 |