Download or read book Commemorative Guidebook to the First Field Conference written by and published by . This book was released on 1981* with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Calibrating Multi dimensional Option Pricing Models written by and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing With Machine Learning written by Daniel Alexandre Bloch and published by . This book was released on 2019 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: An option pricing model is tied to its ability of capturing the dynamics of the underlying spot price process. Its misspecification will lead to pricing and hedging errors. Parametric pricing formula depends on the particular form of the dynamics of the underlying asset. For tractability reasons, some assumptions are made which are not consistent with the multifractal properties of market returns. On the other hand, non-parametric models such as neural networks use market data to estimate the implicit stochastic process driving the spot price and its relationship with contingent claims. When pricing multidimensional contingent claims, or even vanilla options with complex models, one must rely on numerical methods such as partial differential equations, numerical integration methods such as Fourier methods, or Monte Carlo simulations. Further, when calibrating financial models on market prices, a large number of model prices must be generated to fit the model parameters. Thus, one requires highly efficient computation methods which are fast and accurate. Neural networks with multiple hidden layers are universal interpolators with the ability of representing any smooth multidimentional function. As such, supervised learning is concerned with solving function estimation problems. The networks are decomposed into two separate phases, a training phase where the model is optimised off-line, and a testing phase where the model approximates the solution on-line. As a result, these methods can be used in finance in a fast and robust way for pricing exotic options as well as calibrating option prices in view of interpolating/extrapolating the volatility surface. They can also be used in risk management to fit options prices at the portfolio level in view of performing some credit risk analysis. We review some of the existing methods using neural networks for pricing market and model prices, present calibration, and introduce exotic option pricing. We discuss the feasibility of these methods, highlight problems, and propose alternative solutions.

Download or read book Option Pricing and Estimation of Financial Models with R written by Stefano M. Iacus and published by John Wiley & Sons. This book was released on 2011-02-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.

Download or read book Option Pricing in Incomplete Markets written by Yoshio Miyahara and published by World Scientific. This book was released on 2012 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.

Download or read book Distributed Calibration of Option Pricing Models with Multiple Contracts Written on Different Underlying Assets written by Juho Kanniainen and published by . This book was released on 2017 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Think about a situation, where a financial institution has multiple option positions, each written on a different underlying asset, and the unexpected arrival of market-wide news shakes the markets. In the case of such a market-wide news arrival, all the volatility models on different underlyings must be immediately re-calibrated for robust option pricing and hedging. Unfortunately, the calibration of models using data on multiple underlying securities can take too long, especially, if advanced non-affine models without analytical solutions are used. This work demonstrates how multiple independent calibration tasks (on different underlyings) can be efficiently accelerated by Techila, reducing the length of the wall-clock computation time from 7 hours to a few minutes.

Download or read book The Black Scholes and Heston Models for Option Pricing written by Ziqun Ye and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic volatility models on option pricing have received much study following the discovery of the non-at implied surface following the crash of the stock markets in 1987. The most widely used stochastic volatility model is introduced by Heston (1993) because of its ability to generate volatility satisfying the market observations, being non-negative and mean-reverting, and also providing a closed-form solution for the European options. However, little research has been done on Heston model used to price early-exercise options. This presumably is largely due to the absence of a closed-form solution and the increase in computational requirement that complicates the required calibration exercise. This thesis examines the performance of the Heston model versus the Black-Scholes model for the American Style equity option of Microsoft and the index option of S&P 100 index. We employ a finite difference method combined with a Projected Successive Over-relaxation method for pricing an American put option under the Black-Scholes model, while an Alternating Direction Implicit method is utilized to decompose a multi-dimensional partial differential equation into several one dimensional steps under the Heston model. For the calibration of the Heston model, we apply a two step procedure where in the first step we apply an indirect inference method to historical stock prices to estimate diffusion parameters under a probability measure and then use a least squares method to estimate the instantaneous volatility and the market risk premium which are used to switch from working under the probability measure to working under the risk-neutral measure. We find that option price is positively related with the value of the mean reverting speed and the long-term variance. It is not sensitive to the market price of risk and it is negatively related with the risk free rate and the volatility of volatility. By comparing the European put option and the American put option under the Heston model, we observe that their implied volatility generally follow similar patterns. However, there are still some interesting observations that can be made from the comparison of the two put options. First, for the out-of-the-money category, the American and European options have rather comparable implied volatilities with the American options' implied volatility being slightly bigger than the European options. While for the in-the-money category, the implied volatility of the European options is notably higher than the American options and its value exceeds the implied volatility of the American options. We also assess the performance of the Heston model by comparing its result with the result from the Black-Scholes model. We observe that overall the Heston model performs better than the Black-Scholes model. In particular, the Heston model has tendency of underpricing the in-the-money option and overpricing the out-of-the-money option. Whereas, the Black-Scholes model is inclined to underprice both the in-the-money option and the out-of-the-money option.b.

Download or read book Pricing Multi windowed Barrier Options Using Finite Element Method written by Chengshi Ai and published by . This book was released on 2013 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we study pricing multi-windowed barrier options under three different models: Black-Scholes' model, Heston model, and the multi-dimensional Heston model proposed by De Col, Gnoatto and Grasselli. The PDE approach is employed where the option price is deemed as the solution of a partial differential equation. The PDEs arising in the area of option pricing are most parabolic equations. The interesting questions are a) how to deal with the semi-infinite boundary; b) how to determine the boundary conditions when the domain changes with time. Especially we also consider the situation where the Feller condition is violated in the foreign exchange markets, which gives degenerate parabolic equations. We use the finite element method to obtain the numerical results of the PDEs. It is implemented by C++. The main result of this thesis provides a practical scheme in pricing options in a real market scenario. All the coefficients used in the multi-dimensional Heston model can be calibrated once for all according to the real markets. Then the model dimension can be reduced when different types of options are priced.

Download or read book Some Economically Meaningful Option Model Calibration Performance Measures written by Craig A. Friedman and published by . This book was released on 2014 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The desire to more accurately calibrate option pricing models to liquid option prices has been an important driver of the growth of the option pricing literature and practice. However, the most commonly used model calibration accuracy metrics are not designed to reflect the economic consequences of trading based on model prices. To address this shortcoming, we derive, from first principles, in an idealized market setting, new, tractable, and economically meaningful, utility-based, measures of option pricing model calibration performance. We show that when pricing errors are “small,” our measures closely approximate popular percentage pricing error-based metrics. However, our measures can be quite different when model prices are smaller than they ought to be (which can happen when the option pricing model does not properly take into account fat-tailed asset return effects). We compare our measures with widely used metrics and show, via examples using SPX options data, that our new measures better inform us about the economic consequences of model pricing error and thereby better allow us to select among candidate option pricing models.

Download or read book Topics on Option Valuation and Model Calibration written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Implementing Models in Quantitative Finance Methods and Cases written by Gianluca Fusai and published by Springer Science & Business Media. This book was released on 2007-12-20 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.

Download or read book Market Conform Valuation of Options written by Tobias Herwig and published by Taylor & Francis. This book was released on 2006-01-17 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this volume is on the development of new approaches for the market-conform valuation of newly issued derivatives. The first chapter presents a flexible approach to construct the binomial process of the underlying asset price by using a simultaneously backward and forward induction algorithm. This framework can be used to price and hedge a wide range of plain-vanilla and exotic options. In the second chapter this new approach is compared to existing models using a sample of plain-vanilla options, American call options and European Barrier options from two competing markets. In the third chapter new methods to value American-style options via Monte Carlo simulations in accordance with given market prices are discussed. After a short introduction to Monte Carlo methods, two new approaches are proposed. These new frameworks are illustrated via pricing examples for standard American put options.

Download or read book A Time Series Approach to Option Pricing written by Christophe Chorro and published by Springer. This book was released on 2014-12-04 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.

Download or read book Analysis Geometry and Modeling in Finance written by Pierre Henry-Labordere and published by CRC Press. This book was released on 2008-09-22 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing is the first book that applies advanced analytical and geometrical methods used in physics and mathematics to the financial field. It even obtains new results when only approximate and partial solutions were previously available.Through the problem of option pricing, th

Download or read book Calibration Risk for Exotic Options written by Kai Detlefsen and published by . This book was released on 2017 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Option pricing models are calibrated to market data of plain vanillas by minimization of an error functional. From the economic viewpoint, there are several possibilities to measure the error between the market and the model. These different specifications of the error give rise to different sets of calibrated model parameters and the resulting prices of exotic options vary significantly. These price differences often exceed the usual profit margin of exotic options.We provide evidence for this calibration risk in a time series of DAX implied volatility surfaces from April 2003 to March 2004. We analyze in the Heston and in the Bates model factors influencing these price differences of exotic options and finally recommend an error functional. Moreover, we determine the model risk of these two stochastic volatility models for the time series and consider its relation to calibration risk.

Download or read book Manufacturing and Managing Customer Driven Derivatives written by Dong Qu and published by John Wiley & Sons. This book was released on 2016-01-28 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: Manufacturing and Managing Customer-Driven Derivatives Manufacturing and Managing Customer-Driven Derivatives sheds light on customer-driven derivative products and their manufacturing process, which can prove a complicated topic for even experienced financial practitioners. This authoritative text offers up-to-date knowledge and practices across a broad range of topics that address the entire manufacturing, pricing and risk management process, including practical knowledge and industrial best practices. This resource blends quantitative and business perspectives to provide an in-depth understanding of the derivative risk management skills that are necessary to adopt in the competitive financial industry. Manufacturing and managing customer-driven derivative products have become more complex due to macro factors such as the multi-curve environments triggered by the recent financial crises, stricter regulatory requirements of consistent modelling and managing frameworks, and the need for risk/reward optimisation. Explore the fundamental components of the derivatives business, including equity derivatives, interest rates derivatives, real estate derivatives, and real life derivatives, etc. Examine the life cycle of manufacturing derivative products and practical pricing models Deep dive into a wide range of customer-driven structured derivative products, their investment or hedging payoff features and associated risk exposures Examine the implications of changing regulatory standards, which can increase costs in the banking sector Discover practical yet sophisticated product analysis, quantitative modeling, infrastructure integration, risk analysis, and hedging analysis Gain insight on how banks should handle complex derivatives products Manufacturing and Managing Customer-Driven Derivatives is an essential guide for quants, structurers, derivatives traders, risk managers, business executives, insurance industry professionals, hedge fund managers, academic lecturers, and financial math students who are interested in looking at the bigger picture of the manufacturing, pricing and risk management process of customer-driven derivative transactions.