Download or read book Nonparametric Estimation of Risk Neutral Densities written by Maria Grith and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density. The first estimator is a kernel smoother of the second derivative of call prices, while the second procedure applies kernel type smoothing in the implied volatility domain. In the conceptually different third approach we assume the existence of a stochastic discount factor (pricing kernel) which establishes the risk neutral density conditional on the physical measure of the underlying asset. Via direct series type estimation of the pricing kernel we can derive an estimate of the risk neutral density by solving a constrained optimization problem. The methods are compared using European call option prices. The focus of the presentation is on practical aspects such as appropriate choice of smoothing parameters in order to facilitate the application of the techniques.
Download or read book A New Nonparametric Estimate of the Risk Neutral Density with Application to Variance Swap written by Liyuan Jiang and published by . This book was released on 2018 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop a new nonparametric approach for estimating the risk-neutral density of asset price and reformulate its estimation into a double-constrained optimization problem. We implement our approach in R and evaluate it using the S&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the Normal Inverse Gaussian distribution. More specifically, our approach is capable of recovering option prices much better over a broad spectrum of strikes and expirations. While the other methods essentially fail for long-term options (1 year or 2 years to maturity), our approach still works reasonably well. As an application, we use the proposed density estimator to price long-term variance swaps, and our prices match reasonably well with those of the variance future downloaded from the Chicago Board Options Exchange website.
Download or read book Estimation of Risk Neutral Densities Using Positive Convolution Approximation written by Oleg Bondarenko and published by . This book was released on 2014 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a new nonparametric method for estimating the conditional risk-neutral density (RND) from a cross-section of option prices. The idea of the method is to fit option prices by finding the optimal density in a special admissible set. The admissible set consists of functions, each of which may be represented as a convolution of a positive kernel with another density. The method is termed the Positive Convolution Approximation (PCA). The important properties of PCA are that it 1) is completely agnostic about the data generating process, 2) controls against overfitting while allowing for small samples, 3) always produces arbitrage-free estimators, and 4) is computationally simple. In a Monte-Carlo experiment, PCA is compared to several popular methods: mixtures of lognormals (with one, two, and three lognormals), Hermite polynomials, two regularization methods (for the RND and for implied volatilities), and sigma shape polynomials. PCA is found to be a promising alternative to the competitors.
Download or read book Recovering Risk Neutral Densities written by Oleg Bondarenko and published by . This book was released on 2008 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a novel nonparametric method to recover the implied risk-neutral density (RND) from option prices. The main advantages of this method are that it 1) is almost completely agnostic about the true underlying process, 2) controls against overfitting while allowing for small samples, 3) always results in sensible arbitrage-free distributions, 4) estimates the RND over the observable range of strikes only, without involving any extrapolation of density in the tails, 5) is computationally very simple, and 6) can be used to estimate multivariate RNDs. In an empirical application, the new method is implemented on the Samp;P Index options data over the period from 1991 to 1995. To characterize shapes of the Index's RNDs the paper uses the percentile moments which overcome unobservability of the tails of a distribution. The implied RNDs exhibit persistent negative skewness and excessive peakedness. The departures from lognormality become more pronounced as option maturity increases. Day-to-day variation of the RNDs is found to be related to the recent performance of the Index. In particular, on trading days when the Index declines the implied RNDs are more skewed and peaked than when the Index advances. Finally, the implied probabilities of extreme outcomes are also estimated.
Download or read book Nonparametric Pricing of Multivariate Contingent Claims written by Joshua V. Rosenberg and published by . This book was released on 2006 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from the method of copulas allow the multivariate risk-neutral density to be written as a product of marginal risk-neutral densities and a risk-neutral dependence function. A technique to price contingent claims can be developed using non-parametrically estimated marginal risk-neutral densities (based on options data) and a non-parametric dependence function (based on historical return data).Non-parametric estimation eliminates the pricing biases that result from incorrect parametric assumptions such as lognormality. The technique generates fitted multivariate contingent claim prices that are consistent with prices of traded univariate options. Under some general conditions, the objective and risk-neutral dependence functions are identical, which justifies the use of historical return data for the non-parametric dependence function, so that no data are required on traded multivariate claims.
Download or read book Parametric Estimation of Risk Neutral Density Functions written by Maria Grith and published by . This book was released on 2010 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonparametric Density Estimation written by Luc Devroye and published by New York ; Toronto : Wiley. This book was released on 1985-01-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous, systematic treatment of density estimates, their construction, use and analysis with full proofs. It develops L1 theory, rather than the classical L2, showing how L1 exposes fundamental properties of density estimates masked by L2.
Download or read book Three Essays on Estimation of Risk Neutral Measures Using Option Pricing Models written by Seung Hwan Lee and published by . This book was released on 2008 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This dissertation develops two new parametric and nonparametric methods for estimating risk-neutral measures (RNM) which embody important information about market participants' sentiments concerning prices of the underlying asset in the future, and investigates empirical performance of parametric RNM estimation methods. The first essay, "Estimation of Risk Neutral Measures using the Generalized Two-Factor Log-Stable Option Pricing Model", constructs a simple representative agent model to provide a theoretical framework for the log-stable option pricing model and then implements a new parametric method for estimating the RNM using a generalized two-factor log-stable option pricing model. Under the generalized two-factor log-stable uncertainty assumption, the RNM for the log of price is a convolution of two exponentially tilted stable distributions. The generalized two-factor log-stable RNM provides a sufficiently accurate tool for estimating the RNM from observed option prices even if the log-stable assumption might not be satisfied. I estimate the RNM using the S & P 500 index options and find that the generalized two-factor log-stable model gives better performance than alternative models in fitting the observed option prices. The second essay, "Parametric Risk Neutral Measure Estimation Methods: A Horse Race", implements 12 parametric RNM estimation methods by means of the closed-form or characteristic function of RNM distributions and then compares the empirical performance under three criteria - -the root mean squared error (RMSE), likelihood ratio (LR), and the root mean integrated squared error (RMISE). The empirical results show that the generalized two-factor log-stable model outperforms other alternative parametric RNM estimation methods. The third essay, "Nonparametric Estimation of Risk-Neutral Measures using Quartic B-Spline CDFs with Power Tails", proposes a new nonparametric (BSP) method. I model a RNM cumulative distribution function (CDF) using quartic B-splines with power tails so that the resulting RNM probability density function (PDF) has continuity C2 and arbitrage-free properties. Since the number of knots is selected optimally in constructing the quartic B-spline RNM CDF, my method avoids both overfitting and oversmoothing. To improve computational efficiency and accuracy I introduce a 3-step RNM estimation procedure that transforms a nonlinear optimization problem into a convex quadratic program, which is efficiently solved by numerical optimization software.
Download or read book Nonparametric Econometric Methods written by Qi Li and published by Emerald Group Publishing. This book was released on 2009-12-04 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a selection of papers presented initially at the 7th Annual Advances in Econometrics Conference held on the LSU campus in Baton Rouge, Louisiana during November 14-16, 2008. This work is suitable for those who wish to familiarize themselves with nonparametric methodology.
Download or read book Handbook of Computational Finance written by Jin-Chuan Duan and published by Springer Science & Business Media. This book was released on 2011-10-25 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.
Download or read book Introduction to Nonparametric Estimation written by Alexandre B. Tsybakov and published by Springer Science & Business Media. This book was released on 2008-10-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Developed from lecture notes and ready to be used for a course on the graduate level, this concise text aims to introduce the fundamental concepts of nonparametric estimation theory while maintaining the exposition suitable for a first approach in the field.
Download or read book Option Implied Objective Measures of Market Risk written by Matthias Leiss and published by . This book was released on 2016 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foster and Hart (2009) introduce an objective measure of the riskiness of an asset that implies a bound on how much of one's wealth is 'safe' to invest in the asset while (a.s.) guaranteeing no-bankruptcy. In this study, we translate the Foster-Hart measure from static and abstract gambles to dynamic and applied finance using nonparametric estimation of risk-neutral densities from S&P 500 call and put option prices covering 2003 to 2013. The dynamics of the resulting 'option-implied Foster-Hart bound' are assessed in light of other well-known option-implied risk measures including value at risk, expected shortfall and risk-neutral volatility, as well as high moments of the densities and several industry measures. Rigorous variable selection reveals that the new measure is a significant predictor of (large) ahead-return downturns. Furthermore, it grasps more characteristics of the risk-neutral probability distributions in terms of moments than other measures and exhibits predictive consistency. The robustness of the risk-neutral density estimation is analyzed via Monte Carlo methods.
Download or read book Nonparametric Finance written by Jussi Klemelä and published by John Wiley & Sons. This book was released on 2018-02-28 with total page 849 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Machine Learning in Finance, With Mathematical Background, Data Visualization, and R Nonparametric function estimation is an important part of machine learning, which is becoming increasingly important in quantitative finance. Nonparametric Finance provides graduate students and finance professionals with a foundation in nonparametric function estimation and the underlying mathematics. Combining practical applications, mathematically rigorous presentation, and statistical data analysis into a single volume, this book presents detailed instruction in discrete chapters that allow readers to dip in as needed without reading from beginning to end. Coverage includes statistical finance, risk management, portfolio management, and securities pricing to provide a practical knowledge base, and the introductory chapter introduces basic finance concepts for readers with a strictly mathematical background. Economic significance is emphasized over statistical significance throughout, and R code is provided to help readers reproduce the research, computations, and figures being discussed. Strong graphical content clarifies the methods and demonstrates essential visualization techniques, while deep mathematical and statistical insight backs up practical applications. Written for the leading edge of finance, Nonparametric Finance: • Introduces basic statistical finance concepts, including univariate and multivariate data analysis, time series analysis, and prediction • Provides risk management guidance through volatility prediction, quantiles, and value-at-risk • Examines portfolio theory, performance measurement, Markowitz portfolios, dynamic portfolio selection, and more • Discusses fundamental theorems of asset pricing, Black-Scholes pricing and hedging, quadratic pricing and hedging, option portfolios, interest rate derivatives, and other asset pricing principles • Provides supplementary R code and numerous graphics to reinforce complex content Nonparametric function estimation has received little attention in the context of risk management and option pricing, despite its useful applications and benefits. This book provides the essential background and practical knowledge needed to take full advantage of these little-used methods, and turn them into real-world advantage. Jussi Klemelä, PhD, is Adjunct Professor at the University of Oulu. His research interests include nonparametric function estimation, density estimation, and data visualization. He is the author of Smoothing of Multivariate Data: Density Estimation and Visualization and Multivariate Nonparametric Regression and Visualization: With R and Applications to Finance.
Download or read book Nonparametric Functional Estimation and Related Topics written by G.G Roussas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.
Download or read book Nonparametric Estimation of Probability Density Functions written by Jugal Kishore Ghorai and published by . This book was released on 1979 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonparametric estimation of probability density functions written by Albert E. Rust and published by . This book was released on 1979 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Option Implied Risk Neutral Distributions and Risk Aversion written by Jens Carsten Jackwerth and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
