Download or read book Asian Options with Jumps written by Marina Marena and published by . This book was released on 2015 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a closed-form formula for the fair value of call and put options written on the arithmetic average of security prices driven by jump diffusion processes displaying (possibly periodical) trend, time varying volatility, and mean reversion. The model allows one for jointly fitting quoted futures curve and the time structure of spot price volatility. Our result extends the no-jump case put forward in [Fusai, G., Marena, M., Roncoroni, A. 2008. Analytical Pricing of Discretely Monitored Asian-Style Options: Theory and Application to Commodity Markets. Journal of Banking and Finance 32 (10), 2033-2045]. A few tests based on commodity price data assess the importance of introducing a jump component on the resulting option prices.
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 Numerical Methods in Finance written by Michèle Breton and published by Springer Science & Business Media. This book was released on 2005-05-06 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: GERAD celebrates this year its 25th anniversary. The Center was created in 1980 by a small group of professors and researchers of HEC Montreal, McGill University and of the Ecole Polytechnique de Montreal. GERAD's activities achieved sufficient scope to justify its conversion in June 1988 into a Joint Research Centre of HEC Montreal, the Ecole Polytechnique de Montreal and McGill University. In 1996, the U- versite du Quebec a Montreal joined these three institutions. GERAD has fifty members (professors), more than twenty research associates and post doctoral students and more than two hundreds master and Ph.D. students. GERAD is a multi-university center and a vital forum for the devel- ment of operations research. Its mission is defined around the following four complementarily objectives: • The original and expert contribution to all research fields in GERAD's area of expertise; • The dissemination of research results in the best scientific outlets as well as in the society in general; • The training of graduate students and post doctoral researchers; • The contribution to the economic community by solving important problems and providing transferable tools.
Download or read book American Style Asian Options Under Jump Diffusion Processes written by Saize Stefane Draiva and published by LAP Lambert Academic Publishing. This book was released on 2015-12-16 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we derive the analytical solutions to the American-style Asian Options under jump-diffusion processes. The similar problem was studied by Hansen and Jorgensen (2000), but they considered the diffusion case. First of all we transform the problem into one-state variable problem (the dual problem). To this new problem, we find its general analytical solution by using theories from Hansen and Jorgensen (2000), Merton (1976) and H. Pham. Also we derive the analytical solutions to the particular cases, when the average is geometric and arithmetic. In the arithmetic average case, the one-state variable is not a geometric Brownian motion, so we approximate it to a geometric Brownian motion by using the Wilkisson aproximation. At the end of this book we have some numerical results comparing the earlier exercise boundaries in diffusion and jump-diffusion cases.
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 Monte Carlo Methods in Financial Engineering written by Paul Glasserman and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Paul Glasserman has written an astonishingly good book that bridges financial engineering and the Monte Carlo method. The book will appeal to graduate students, researchers, and most of all, practicing financial engineers [...] So often, financial engineering texts are very theoretical. This book is not." --Glyn Holton, Contingency Analysis
Download or read book Numerical Schemes for Pricing Asian Options Under State Dependent Regime Switching Jump Diffusion Models written by Duy-Minh Dang and published by . This book was released on 2018 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose numerical schemes for pricing Asian options when the underlying asset price follows a very general state-dependent regime-switching jump-diffusion process. Under this model, the price of the option can be obtained by solving a highly complex system of coupled two-dimensional parabolic partial integro-differential equations (PIDEs) via iterative techniques. One of the proposed schemes is provably convergent to the solution of the system of PIDEs. In addition, by treating the coupling and integral terms explicitly, over each iteration of the scheme, the pricing problem under this scheme can be partitioned into independent pricing sub-problem, with communication at the end of the iteration. Hence, this method allows for a very natural and easy-to-implement, yet efficient, parallelization of the solution process on multi-core architectures. We illustrate the accuracy and efficiency of the proposed methods by several numerical examples.
Download or read book Quantitative Analysis in Financial Markets written by Marco Avellaneda and published by World Scientific. This book was released on 1999 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lectures presented at the Courant Institute's Mathematical Finance Seminar.
Download or read book On Approximating Deep In the Money Asian Options Under Exponential L vy Processes written by Leonard Tchuindjo and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This note proposes a new approach of valuing deep in-the-money fixed strike and discretely monitoring arithmetic Asian options. This new approach prices Asian options whose underlying asset price evolves according to the exponential of a Lévy process as a weighted sum of European options. Numerical results from experimenting on three different types of Lévy processes -- a diffusion process, a jump diffusion process, and a pure jump process -- illustrate the accuracy of the approach.
Download or read book Pricing Vulnerable Asian Options with the Correlated Credit Risk Under Jump diffusion Process written by 張椀筑 and published by . This book was released on 2019 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Commodity Asian Option Pricing and Simulation in a 4 Factor Model with Jump Clusters written by Riccardo Brignone and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean reversion, stochastic volatility, convenience yield and presence of jump clustering are well documented salient features of commodity markets, where Asian options are very popular. We propose a model which takes into account all these stylized features. We first state our model under the historical measure, then, after introducing a structure preserving change of measure, we provide a risk-neutral version of the same model and we show how to price geometric and arithmetic Asian options. To this end, we derive semi-closed formulas for the geometric Asian options price and develop a computationally efficient simulation scheme for the price process, allowing to price the arithmetic counterparts using control variate technique. Finally, we propose a simple econometric experiment to document presence of jump clusters in commodity prices and evaluate the performances of the proposed simulation scheme on some parameter sets calibrated on real data.
Download or read book Modern Problems in Insurance Mathematics written by Dmitrii Silvestrov and published by Springer. This book was released on 2014-06-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of 21 papers presented at the International Cramér Symposium on Insurance Mathematics (ICSIM) held at Stockholm University in June, 2013. The book comprises selected contributions from several large research communities in modern insurance mathematics and its applications. The main topics represented in the book are modern risk theory and its applications, stochastic modelling of insurance business, new mathematical problems in life and non-life insurance and related topics in applied and financial mathematics. The book is an original and useful source of inspiration and essential reference for a broad spectrum of theoretical and applied researchers, research students and experts from the insurance business. In this way, Modern Problems in Insurance Mathematics will contribute to the development of research and academy–industry co-operation in the area of insurance mathematics and its applications.
Download or read book A Way to Garden written by Margaret Roach and published by Timber Press. This book was released on 2019-04-30 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: “A Way to Garden prods us toward that ineffable place where we feel we belong; it’s a guide to living both in and out of the garden.” —The New York Times Book Review For Margaret Roach, gardening is more than a hobby, it’s a calling. Her unique approach, which she calls “horticultural how-to and woo-woo,” is a blend of vital information you need to memorize and intuitive steps you must simply feel and surrender to. In A Way to Garden, Roach imparts decades of garden wisdom on seasonal gardening, ornamental plants, vegetable gardening, design, gardening for wildlife, organic practices, and much more. She also challenges gardeners to think beyond their garden borders and to consider the ways gardening can enrich the world. Brimming with beautiful photographs of Roach’s own garden, A Way to Garden is practical, inspiring, and a must-have for every passionate gardener.
Download or read book Stochastic Finance written by Jan Vecer and published by CRC Press. This book was released on 2011-01-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested text provides a deep understanding of derivative contracts. Unlike much of the existing literature, the book treats price as a number of units of one asset needed for an acquisition of a unit of another asset instead of expressing prices in dollar terms exclusively. This numeraire approach leads to simpler pricing options for complex products, such as barrier, lookback, quanto, and Asian options. With many examples and exercises, the text relies on intuition and basic principles, rather than technical computations.
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 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 Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
