Download or read book Analysis of Parametric and Non Parametric Option Pricing Models written by Qiang Luo and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, a closed-form analytical solution of option price under the Bi-Heston model is derived. Through empirical analysis, the advantages and disadvantages of the parametric pricing model are compared and analysed with those of the non-parametric model. The analysis shows that: (1) the parametric pricing model significantly outperforms the machine learning model in terms of in-sample pricing effects, while the Bi-Heston model slightly outperforms the Heston model. (2) In terms of out-of-sample pricing, the machine learning model is inferior to the parametric model for call options, while the Bi-Heston model is significantly better than the other two models for put options, and the other two models are similar. (3) In the robustness analysis of the three pricing models, the machine learning model shows strong instability, while the Bi-Heston model shows a more stable side.

Download or read book Option Pricing with Model Guided Nonparametric Methods written by Jianqing Fan and published by . This book was released on 2009 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parametric option pricing models are largely used in Finance. These models capture several features of asset price dynamics. However, their pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches that learn and correct empirically the pricing errors. In this paper, we propose a new nonparametric method for pricing derivatives assets. Our method relies on the state price distribution instead of the state price density because the former is easier to estimate nonparametrically than the latter. A parametric model is used as an initial estimate of the state price distribution. Then the pricing errors induced by the parametric model are fitted nonparametrically. This model-guided method estimates the state price distribution nonparametrically and is called Automatic Correction of Errors (ACE). The method is easy to implement and can be combined with any model-based pricing formula to correct the systematic biases of pricing errors. We also develop a nonparametric test based on the generalized likelihood ratio to document the efficacy of the ACE method. Empirical studies based on Samp;P 500 index options show that our method outperforms several competing pricing models in terms of predictive and hedging abilities.

Download or read book An Empirical Comparison of Alternative Option Pricing Models written by Ta-Peng Wu and published by . This book was released on 2000 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonparametric and Semiparametric Models written by Wolfgang Karl Härdle and published by Springer Science & Business Media. This book was released on 2012-08-27 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity.

Download or read book Parametric and Non parametric Option Hedging and Estimation Based on Hedging Error Minimization written by Xiaoyi Chen and published by . This book was released on 2020 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past few decades, option pricing accuracy has always been a standard criterion in gauging the performance of model parameter estimates. However, as a primary concern for option market makers, option hedging activity receives much less attention than pricing. Since option hedging strives to eliminate risks of market makers' portfolio positions in practice, it might be a more sensible measure in evaluating model estimates. In the first part of this thesis, a parameter estimation procedure based on minimizing the risks accumulated over the lifetime of an option is proposed. More specifically, a loss function which involves option pricing and hedging strategies is first defined to evaluate the cumulative hedging error(CHE). Then, after a simulation study assuming the Black-Scholes(BS) model for stock dynamics and option prices, an estimation method based on minimizing CHE is compared with maximum likelihood estimation(MLE) and implied estimation under three different model settings: the Black-Scholes model, the Merton jump diffusion, and the Heston stochastic volatility model. This comparison is conducted using an empirical study consisting of multiple datasets of individual stocks and options spanning 2011-2014 with the back-testing procedure. The second part of this thesis tries to mitigate the model-dependent feature of the first part, allowing flexible smoothing spline estimates for the option pricing curves. There are shape constraints induced by the arbitrage-free conditions of pricing options. Therefore, the form of the smoothing spline is carefully chosen to satisfy the constraints. In addition, certain transformation to the inputs of the pricing curve is performed to reduce dimensions. Under such strict constraints, we propose an option pricing curve which is composed of a weighted average between the Black-Scholes pricing function and a constrained cubic spline function. The resulting pricing and hedging strategies generated by the weighted curve estimator are then used to evaluate the previously defined cumulative hedging error(CHE). The back-testing results show that in general, smaller cumulative hedging error for real equity market data is achieved by the proposed hedging error minimization method, compared with traditional estimation methods.

Download or read book Handbook Of Financial Econometrics Mathematics Statistics And Machine Learning In 4 Volumes written by Cheng Few Lee and published by World Scientific. This book was released on 2020-07-30 with total page 5053 pages. Available in PDF, EPUB and Kindle. Book excerpt: This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.

Download or read book Model guided Nonparametric Option Pricing written by Wentao Yan and published by . This book was released on 2009 with total page 166 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 Market Conform Valuation of Options written by Tobias Herwig and published by Springer Science & Business Media. This book was released on 2006-03-12 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1 The Area of Research In this thesis, we will investigate the 'market-conform' pricing of newly issued contingent claims. A contingent claim is a derivative whose value at any settlement date is determined by the value of one or more other underlying assets, e. g. , forwards, futures, plain-vanilla or exotic options with European or American-style exercise features. Market-conform pricing means that prices of existing actively traded securities are taken as given, and then the set of equivalent martingale measures that are consistent with the initial prices of the traded securities is derived using no-arbitrage arguments. Sometimes in the literature other expressions are used for 'market-conform' valuation - 'smile-consistent' valuation or 'fair-market' valuation - that describe the same basic idea. The seminal work by Black and Scholes (1973) (BS) and Merton (1973) mark a breakthrough in the problem of hedging and pricing contingent claims based on no-arbitrage arguments. Harrison and Kreps (1979) provide a firm mathematical foundation for the Black-Scholes- Merton analysis. They show that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure. Under this mea sure the normalized security price process forms a martingale and so securities can be valued by taking expectations. If the securities market is complete, then the equivalent martingale measure and hence the price of any security are unique.

Download or read book A Simple Non Parametric Approach to Bond Futures Option Pricing written by Michael J. Stutzer and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: When used to price popular bond futures options, the Black model is subject to a moneyness bias similar to the Black-Scholes stock index option bias. It is shown that a suitably modified version of Stutzer's canonical stock option pricing model (Stutzer, J.Finance, 1996, 1633-52 ) also helps explain the former bias. This paper further extends the entropic approach to asset pricing theory and estimation developed in the aforementioned paper, in J.Econometrics, 1995, 367-97 and in Econometrica, 1997, 861-74.

Download or read book Essays on Option Valuation written by Li Xia and published by . This book was released on 2001 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Parameter Functions for Option Pricing written by Christakis Charalambous and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend the benchmark nonlinear deterministic volatility regression functions of Dumas et al. (1998) to provide a semi-parametric method where an enhancement of the implied parameter values is used in the parametric option pricing models. Besides volatility, skewness and kurtosis of the asset return distribution can also be enhanced. Empirical results, using closing prices of the Samp;P 500 index call options (in one day ahead out-of-sample pricing tests), strongly support our method that compares favorably with a model that admits stochastic volatility and random jumps. Moreover, it is found to be superior in various robustness tests. Our semi-parametric approach is an effective remedy to the curse of dimensionality presented in nonparametric estimation and its main advantage is that it delivers theoretically consistent option prices and hedging parameters. The economic significance of the approach is tested in terms of hedging, where the evaluation and estimation loss functions are aligned.

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 Options Pricing Via Statistical Learning Techniques written by Panayiotis C. Andreou and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We explore the pricing performance of Support Vector Regression for pricing S&P 500 index call options. Support Vector Regression is a novel nonparametric methodology that has been developed in the context of statistical learning theory and until now it has been practically neglected in financial econometric applications. This new method is compared with Parametric Options Pricing Models using standard implied parameters and parameters derived via Deterministic Volatility Functions. The empirical analysis has shown promising results for the Support Vector Regression approach.

Download or read book Barrier Option Pricing with Nonparametric ACE Methods written by Chengzhan Chi and published by . This book was released on 2013 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are a variety of parametric and nonparametric option pricing models commonly used in Finance. A combination of them can enhance the pricing performance significantly. Specifically, one proposes to fit the data with a parametric method and then correct the pricing errors empirically with a nonparametric learning approach. This thesis extends Fan and Mancini's (2009) model-guided nonparametric method to barrier option pricing using market traded European option data. Adopting automatic correction of errors (ACE) method to estimate the risk neutral conditional survivor function, by which the pricing error of the initial parametric estimates is captured nonparametrically, enables the nonparametric pricing procedure to value a barrier option as a sum of sequence of European options. As a byproduct from the valuation process, this thesis also provides a modified fractional fast Fourier transform technique compute the characteristic function of the running maximum log-price of the underlying asset nonparametrically through the calibrated survivor functions.

Download or read book Nonparametric Econometrics written by Qi Li and published by Princeton University Press. This book was released on 2011-10-09 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, up-to-date textbook on nonparametric methods for students and researchers Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data—nominal and ordinal—in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types—continuous, nominal, and ordinal—within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.

Download or read book Handbook of Quantitative Finance and Risk Management written by Cheng-Few Lee and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 1700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.