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Asymptotic Distribution Expansions In Option Pricing
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Book Synopsis Asymptotic Distribution Expansions in Option Pricing by : Daniel Giamouridis
Download or read book Asymptotic Distribution Expansions in Option Pricing written by Daniel Giamouridis and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article extends an option pricing model and studies the properties of implied probability distribution functions (PDFs) recovered from American interest rate futures options. The model relaxes the restricting assumption of lognormally distributed returns accommodating a wide variety of implied PDFs shapes. Non-normal skewness and kurtosis are found to contribute significantly to estimating more precise implied densities. The model achieves good in-sample accuracy, similar to that achieved by alternative approaches. The recovered implied PDFs are, finally, found to be closer to a median PDF estimated using a number of alternative techniques.
Book Synopsis A Note on Asymptotic Expansion for Option Pricing with Interacting Assets by : Elisa Mastrogiacomo
Download or read book A Note on Asymptotic Expansion for Option Pricing with Interacting Assets written by Elisa Mastrogiacomo and published by . This book was released on 2018 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present paper we develop an asymptotic expansion method for a suitable class of stochastic differential equation, using methods by S. Watanabe (1987) (see also Ikeda and Watanabe (1989) and Lutkebohmert (2004)). Such asymptotic expansion is calculated around the multidimensional Black-Scholes model for interacting assets.
Book Synopsis Asymptotic Chaos Expansions in Finance by : David Nicolay
Download or read book Asymptotic Chaos Expansions in Finance written by David Nicolay and published by Springer. This book was released on 2014-11-25 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface. In principle, they are well suited for pricing and hedging vanilla and exotic options, for relative value strategies or for risk management. In practice however, most SV models lack a closed form valuation for European options. This book presents the recently developed Asymptotic Chaos Expansions methodology (ACE) which addresses that issue. Indeed its generic algorithm provides, for any regular SV model, the pure asymptotes at any order for both the static and dynamic maps of the implied volatility surface. Furthermore, ACE is programmable and can complement other approximation methods. Hence it allows a systematic approach to designing, parameterising, calibrating and exploiting SV models, typically for Vega hedging or American Monte-Carlo. Asymptotic Chaos Expansions in Finance illustrates the ACE approach for single underlyings (such as a stock price or FX rate), baskets (indexes, spreads) and term structure models (especially SV-HJM and SV-LMM). It also establishes fundamental links between the Wiener chaos of the instantaneous volatility and the small-time asymptotic structure of the stochastic implied volatility framework. It is addressed primarily to financial mathematics researchers and graduate students, interested in stochastic volatility, asymptotics or market models. Moreover, as it contains many self-contained approximation results, it will be useful to practitioners modelling the shape of the smile and its evolution.
Book Synopsis Normal Approximation and Asymptotic Expansions by : Rabi N. Bhattacharya
Download or read book Normal Approximation and Asymptotic Expansions written by Rabi N. Bhattacharya and published by SIAM. This book was released on 2010-11-11 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: -Fourier analysis, --
Book Synopsis Small-time Asymptotics and Expansions of Option Prices Under Levy-based Models by : Ruoting Gong
Download or read book Small-time Asymptotics and Expansions of Option Prices Under Levy-based Models written by Ruoting Gong and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the small-time asymptotics and expansions of call option prices, when the log return processes of the underlying stock prices follow several Levy-based models. To be specific, we derive the time-to-maturity asymptotoc behavior for both at-the-money (ATM, out-of-the-money (OTM) and in-the-money (ITM) call option prices under several jump diffusion models and stochastic volatility models with Levy jumps. In the OTM and ITM cases, we consider a general stochastic volatility model with independent Levy jumps, while in the ATM case, we consider the pure-jump CGMY model with or without an independent Brownian component. An accurate modeling of the option market and asset prices requires a mixture of a continuous diffusive component and a jump component. In this thesis, we first model the log-return process of a fisk asset with a jump diffusion model by combining a stochastic volatility model with an independent pure-jump Levy process. By assuming smoothness conditions on the Levy density away from the origin and a small-time large deviation principle on the stochastic volatility model, we derive the small-time expansions, of arbitrary polynomial order, in time-t, for the tail distribution of the log-return process, and for the call-option price which is not at-the-money. Moreover, our approach allows for a unified treatment of more general payoff functions. As a consequence of our tail expansions, the polynomial expansion in t of the transition density is also obtained under mild conditions. The asymptotic behavior of the ATM call-option prices is more complicated to obtain, and, in general, is given by fractional powers of t, which depends on different choices of the underlying log-return models. Here, we focus on the CGMY model, one of the most popular tempered stable models used in financial modeling. A novel second-order approximation for ATM option prices under the pure-jump CGMY Levy model is derived, and then extended to a model with an additional independent Brownian component. The third-order asymptotic behavior of the ATM option prices as well as the asymptotic behavior of the corresponding Black-Scholes implied volatilities are also addressed.
Book Synopsis Asymptotic Methods for Option Pricing in Finance by : David Krief
Download or read book Asymptotic Methods for Option Pricing in Finance written by David Krief and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we study several mathematical finance problems, related to the pricing of derivatives. Using different asymptotic approaches, we develop methods to calculate accurate approximations of the prices of certain types of options in cases where no explicit formulas are available.In the first chapter, we are interested in the pricing of path-dependent options, with Monte-Carlo methods, when the underlying is modelled as an affine stochastic volatility model. We prove a long-time trajectorial large deviations principle. We then combine it with Varadhan's Lemma to calculate an asymptotically optimal measure change, that allows to reduce significantly the variance of the Monte-Carlo estimator of option prices.The second chapter considers the pricing with Monte-Carlo methods of options that depend on several underlying assets, such as basket options, in the Wishart stochastic volatility model, that generalizes the Heston model. Following the approach of the first chapter, we prove that the process verifies a long-time large deviations principle, that we use to reduce significantly the variance of the Monte-Carlo estimator of option prices, through an asymptotically optimal measure change. In parallel, we use the large deviations property to characterize the long-time behaviour of the Black-Scholes implied volatility of basket options.In the third chapter, we study the pricing of options on realized variance, when the spot volatility is modelled as a diffusion process with constant volatility. We use recent asymptotic results on densities of hypo-elliptic diffusions to calculate an expansion of the density of realized variance, that we integrate to obtain an expansion of option prices and their Black-Scholes implied volatility.The last chapter is dedicated to the pricing of interest rate derivatives in the Levy Libor market model, that generaliszes the classical (log-normal) Libor market model by introducing jumps. Writing the first model as a perturbation of the second and using the Feynman-Kac representation, we calculate explicit expansions of the prices of interest rate derivatives and, in particular, caplets and swaptions.
Book Synopsis Large Deviations and Asymptotic Methods in Finance by : Peter K. Friz
Download or read book Large Deviations and Asymptotic Methods in Finance written by Peter K. Friz and published by Springer. This book was released on 2015-06-16 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
Book Synopsis Asymptotic Expansions of Integrals by : Norman Bleistein
Download or read book Asymptotic Expansions of Integrals written by Norman Bleistein and published by Courier Corporation. This book was released on 1986-01-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excellent introductory text, written by two experts, presents a coherent and systematic view of principles and methods. Topics include integration by parts, Watson's lemma, LaPlace's method, stationary phase, and steepest descents. Additional subjects include the Mellin transform method and less elementary aspects of the method of steepest descents. 1975 edition.
Book Synopsis Asymptotic Methods for Stochastic Volatility Option Pricing -- An Explanatory Study by : Lichen Chen
Download or read book Asymptotic Methods for Stochastic Volatility Option Pricing -- An Explanatory Study written by Lichen Chen and published by . This book was released on 2011 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In this project, we study an asymptotic expansion method for solving stochastic volatility European option pricing problems. We explain the backgrounds and details associated with the method. Specifically, we present in full detail the arguments behind the derivation of the pricing PDEs and detailed calculation in deriving asymptotic option pricing formulas using our own model specifications. Finally, we discuss potential difficulties and problems in the implementation of the methods.
Book Synopsis An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price Under Stochastic Volatility Model by : Takashi Kato
Download or read book An Asymptotic Expansion Formula for Up-and-Out Barrier Option Price Under Stochastic Volatility Model written by Takashi Kato and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate the validity of our approximation method through numerical examples.
Book Synopsis Options Pricing in Incomplete Markets: An Asymptotic Approach by :
Download or read book Options Pricing in Incomplete Markets: An Asymptotic Approach written by and published by . This book was released on 1996 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is explored how incomplete markets can be studied with the help of asymptotics. A compound Poisson model for the stock price is assumed and an expansion for the price of a European option is obtained as the stock price process converges to a geometric Brownian motion. This formulation also permits one to confront statistical uncertainty in the volatility of the stock price, and we show how this uncertainty impacts on the value of the option.
Book Synopsis Asymptotic Expansions for Ordinary Differential Equations by : Wolfgang Wasow
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Download or read book The Journal of Derivatives written by and published by . This book was released on 2001 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Expansions by : E. T. Copson
Download or read book Asymptotic Expansions written by E. T. Copson and published by Cambridge University Press. This book was released on 2004-06-03 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.
Book Synopsis Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications by : Philippe Barbe
Download or read book Asymptotic Expansions for Infinite Weighted Convolutions of Heavy Tail Distributions and Applications written by Philippe Barbe and published by American Mathematical Soc.. This book was released on 2009 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: "January 2009, volume 197, number 922 (Fourth of five numbers)."
Book Synopsis Identification and Inference for Econometric Models by : Donald W. K. Andrews
Download or read book Identification and Inference for Econometric Models written by Donald W. K. Andrews and published by Cambridge University Press. This book was released on 2005-07-04 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2005 volume contains the papers presented in honor of the lifelong achievements of Thomas J. Rothenberg on the occasion of his retirement. The authors of the chapters include many of the leading econometricians of our day, and the chapters address topics of current research significance in econometric theory. The chapters cover four themes: identification and efficient estimation in econometrics, asymptotic approximations to the distributions of econometric estimators and tests, inference involving potentially nonstationary time series, such as processes that might have a unit autoregressive root, and nonparametric and semiparametric inference. Several of the chapters provide overviews and treatments of basic conceptual issues, while others advance our understanding of the properties of existing econometric procedures and/or propose others. Specific topics include identification in nonlinear models, inference with weak instruments, tests for nonstationary in time series and panel data, generalized empirical likelihood estimation, and the bootstrap.
Book Synopsis Generalized Poisson Models and their Applications in Insurance and Finance by : Vladimir E. Bening
Download or read book Generalized Poisson Models and their Applications in Insurance and Finance written by Vladimir E. Bening and published by Walter de Gruyter. This book was released on 2012-06-11 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
