Pricing Of Discretely Sampled Asian Options Under Levy Processes
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Author | : Jiayao Xie |
Publisher | : |
Total Pages | : |
Release | : 2012 |
Genre | : |
ISBN | : |
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.
Author | : Pingping Zeng |
Publisher | : |
Total Pages | : 31 |
Release | : 2015 |
Genre | : |
ISBN | : |
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.
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 | : Roger Lord |
Publisher | : Rozenberg Publishers |
Total Pages | : 211 |
Release | : 2008 |
Genre | : |
ISBN | : 9051709099 |
Author | : Jin E. Zhang |
Publisher | : |
Total Pages | : 48 |
Release | : 2000 |
Genre | : Options (Finance) |
ISBN | : |
Author | : Andrea Roncoroni |
Publisher | : John Wiley & Sons |
Total Pages | : 1076 |
Release | : 2015-02-19 |
Genre | : Business & Economics |
ISBN | : 0470661836 |
Handbook of Multi-Commodity Markets and ProductsOver recent decades, the marketplace has seen an increasing integration, not only among different types of commodity markets such as energy, agricultural, and metals, but also with financial markets. This trend raises important questions about how to identify and analyse opportunities in and manage risks of commodity products. The Handbook of Multi-Commodity Markets and Products offers traders, commodity brokers, and other professionals a practical and comprehensive manual that covers market structure and functioning, as well as the practice of trading across a wide range of commodity markets and products. Written in non-technical language, this important resource includes the information needed to begin to master the complexities of and to operate successfully in today’s challenging and fluctuating commodity marketplace. Designed as a practical practitioner-orientated resource, the book includes a detailed overview of key markets – oil, coal, electricity, emissions, weather, industrial metals, freight, agricultural and foreign exchange – and contains a set of tools for analysing, pricing and managing risk for the individual markets. Market features and the main functioning rules of the markets in question are presented, along with the structure of basic financial products and standardised deals. A range of vital topics such as stochastic and econometric modelling, market structure analysis, contract engineering, as well as risk assessment and management are presented and discussed in detail with illustrative examples to commodity markets. The authors showcase how to structure and manage both simple and more complex multi-commodity deals. Addressing the issues of profit-making and risk management, the book reveals how to exploit pay-off profiles and trading strategies on a diversified set of commodity prices. In addition, the book explores how to price energy products and other commodities belonging to markets segmented across specific structural features. The Handbook of Multi-Commodity Markets and Products includes a wealth of proven methods and useful models that can be selected and developed in order to make appropriate estimations of the future evolution of prices and appropriate valuations of products. The authors additionally explore market risk issues and what measures of risk should be adopted for the purpose of accurately assessing exposure from multi-commodity portfolios. This vital resource offers the models, tools, strategies and general information commodity brokers and other professionals need to succeed in today’s highly competitive marketplace.
Author | : Krzysztof Dębicki |
Publisher | : Springer |
Total Pages | : 256 |
Release | : 2015-08-06 |
Genre | : Mathematics |
ISBN | : 3319206931 |
The book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
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 | : Justin Kirkby |
Publisher | : |
Total Pages | : 33 |
Release | : 2017 |
Genre | : |
ISBN | : |
In general, no analytical formulas exist for pricing discretely monitored exotic options, even when a geometric Brownian motion governs the risk-neutral underlying. While specialized numerical algorithms exist for pricing particular contracts, few can be applied universally with consistent success and with general Lévy dynamics. This paper develops a general methodology for pricing early exercise and exotic financial options by extending the recently developed PROJ method. We are able to efficiently obtain accurate values for complex products including Bermudan/American options, Bermudan barrier options, survival probabilities and credit default swaps by value recursion, European barrier and lookback/hindsight options by density recursion, and arithmetic Asian options by characteristic function recursion. This paper presents a unified approach to tackling these and related problems. Algorithms are provided for each option type, along with a demonstration of convergence. We also provide a large set of reference prices for exotic, American and European options under Black-Scholes-Merton, Normal Inverse Gaussian, Kou's double exponential jump diffusion, Variance Gamma, KoBoL/CGMY and Merton's jump diffusion models.
Author | : Yoshio Miyahara |
Publisher | : World Scientific |
Total Pages | : 200 |
Release | : 2012 |
Genre | : Electronic books |
ISBN | : 1848163487 |
This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric L(r)vy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problem