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Book Estimation of Generalized Diffusions from Option Prices

Download or read book Estimation of Generalized Diffusions from Option Prices written by Gurupdesh S. Pandher and published by . This book was released on 2011 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops option-based estimators of the diffusion using the Estimating Function approach. The resulting estimators have a generic structure that applies to a wide class of state-time separable diffusions found in option pricing models. Our methodology differs from the related literature in a number of ways. First, inferences regarding the diffusion are made jointly from option and asset prices and Estimating Function theory identifies the optimal estimating equation for the estimators. Second, the method is distribution-free in the sense that estimation of the diffusion's transition density is not required. Lastly, the proposed option diffusion estimators are robust to distributional assumptions on the underlying asset prices (e.g. log-normality) as their asymptotic convergence and normality is established under conditional first and second moment assumptions.Monte-Carlo analysis verifies the accuracy and efficiency of the option diffusion estimators and resolves important sample design issues. Applications of the proposed option diffusion estimators to empirical option pricing, quantifying divergence between option and asset prices, and investment strategies are discussed.

Book Volatility Estimation and Option Pricing

Download or read book Volatility Estimation and Option Pricing written by Jian Zou and published by . This book was released on 2009 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Inversion of Option Prices for Implied Risk Neutral Probability Density Functions

Download or read book Inversion of Option Prices for Implied Risk Neutral Probability Density Functions written by Chen Wang and published by . This book was released on 2014 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper applies classic linear inverse theory to the estimation of the implied risk neutral probability density function (PDF) from option prices. To overcome non-uniqueness and instability inherent in the option inverse problem, smoothness requirement for the shape of a PDF and an initial model are introduced by a penalty function. Positivity constraints are included as a hard bond on the PDF values. Then the option inverse problem becomes a non-negative least-squares problem which can be solved by the classic methods such as the non-negative least squares program of Lawson and Hanson (1974). The best solution is not the solution that gives best fit, but the solution that gives the optimal trade-off between the goodness of fit and smoothness of the estimated risk natural PDF. The proposed inversion technique is compared to the models of Black-Scholes (BS), a mixture of two lognormals (MLN), Jarrow and Rudd's Edgeworth expansion (JR), and jump diffusion (JD) for the estimation of the PDF from the option prices associated with the September 2007 NYMEX natural gas futures. It is found that the inversion technique not only gives best goodness of fit, but also the significantly better model resolution. BS, JD and MLN models basically cannot resolve the densities far away from the strikes where option prices are observed and can resolve long wavelength features of the densities inside the strikes where option prices are observed. On the other hand, the inversion model can resolve not only the significant details of the densities inside the strikes where option prices are observed, but also the long wavelength features of the densities away from the strikes where option prices are observed. The empirical study for the last three months of the September 2007 futures contract shows that the shapes of the estimated PDFs become more symmetric as the futures contract is closer to the expiration date. The dispersion of the estimated PDFs decreases with decreasing the time to expire, indicating the resolution of uncertainty with time.

Book General Equilibrium Option Pricing Method Theoretical and Empirical Study

Download or read book General Equilibrium Option Pricing Method Theoretical and Empirical Study written by Jian Chen and published by Springer. This book was released on 2018-04-10 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book mainly addresses the general equilibrium asset pricing method in two aspects: option pricing and variance risk premium. First, volatility smile and smirk is the famous puzzle in option pricing. Different from no arbitrage method, this book applies the general equilibrium approach in explaining the puzzle. In the presence of jump, investors impose more weights on the jump risk than the volatility risk, and as a result, investors require more jump risk premium which generates a pronounced volatility smirk. Second, based on the general equilibrium framework, this book proposes variance risk premium and empirically tests its predictive power for international stock market returns.

Book Option Pricing Based on the Generalized Lambda Distribution

Download or read book Option Pricing Based on the Generalized Lambda Distribution written by Charles J. Corrado and published by . This book was released on 2001 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized lambda distribution is proposed as a useful model for security price distributions. Originally used to generate random variables with varied skewness and kurtosis values in Monte Carlo simulations, proposed financial applications include estimation of state price densities from option prices and VaR simulations based on a multivariate version of the generalized lambda distribution.

Book An Option Pricing Formula for the GARCH Diffusion Model

Download or read book An Option Pricing Formula for the GARCH Diffusion Model written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we derive an analytical closed-form approximation for European option prices under the GARCH diffusion model, where the price is driven by a geometric process and the variance by an uncorrelated mean reverting geometric process. This result has several important implications. First and foremost, these conditional moments allow us to obtain an analytical closed-form approximation for European option prices under the GARCH diffusion model. This approximation can be easily implemented in any standard software package. As we will show using Monte Carlo simulations, this approximation is very accurate across different strikes and maturities for a large set of reasonable parameters. Secondly, our analytical approximation allows to easily study volatility surfaces induced by GARCH diffusion models. Thirdly, the conditional moments of the integrated variance implied by the GARCH diffusion process generalize the conditional moments derived by Hull and White (1987) for log-normal variance processes. Finally, the conditional moments of the integrated variance can be used to estimate the continuous time parameters of the GARCH diffusion model using high frequency data. The thesis is organized as follows. Chapter 1 introduces stochastic volatility option pricing models and discusses in details the GARCH diffusion model and its properties. Chapter 2 presents the analytical approximation formula to price European options under the GARCH diffusion model. Using Monte Carlo simulations, we verify the accuracy of the approximation across different strike prices and times to maturity for different parameter choices. We investigate differences between option prices under the GARCH diffusion and the Black and Scholes model. Then, we qualitatively study implied volatility surfaces induced by the GARCH diffusion. Chapter 3 studies the accuracy of the inference results on the GARCH diffusion model based on the Nelson's theory. Using such a procedure, we fit the GARCH diffusi.

Book Estimating Option Pricing Models Using a Characteristic Function based Linear State Space Representation

Download or read book Estimating Option Pricing Models Using a Characteristic Function based Linear State Space Representation written by Herman Peter Boswijk and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a novel filtering and estimation procedure for parametric option pricing models driven by general affine jump-diffusions. Our procedure is based on the comparison between an option-implied, model-free representation of the conditional log-characteristic function and the model-implied conditional log-characteristic function, which is functionally affine in the model's state vector. We formally derive an associated linear state space representation and establish the asymptotic properties of the corresponding measurement errors. The state space representation allows us to use a suitably modified Kalman filtering technique to learn about the latent state vector and a quasi-maximum likelihood estimator of the model parameters, which brings important computational advantages. We analyze the finite-sample behavior of our procedure in Monte Carlo simulations. The applicability of our procedure is illustrated in two case studies that analyze S&P 500 option prices and the impact of exogenous state variables capturing Covid-19 reproduction and economic policy uncertainty.

Book Pathwise Estimation and Inference for Diffusion Market Models

Download or read book Pathwise Estimation and Inference for Diffusion Market Models written by Nikolai Dokuchaev and published by CRC Press. This book was released on 2019-03-26 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pathwise estimation and inference for diffusion market models discusses contemporary techniques for inferring, from options and bond prices, the market participants' aggregate view on important financial parameters such as implied volatility, discount rate, future interest rate, and their uncertainty thereof. The focus is on the pathwise inference methods that are applicable to a sole path of the observed prices and do not require the observation of an ensemble of such paths. This book is pitched at the level of senior undergraduate students undertaking research at honors year, and postgraduate candidates undertaking Master’s or PhD degree by research. From a research perspective, this book reaches out to academic researchers from backgrounds as diverse as mathematics and probability, econometrics and statistics, and computational mathematics and optimization whose interest lie in analysis and modelling of financial market data from a multi-disciplinary approach. Additionally, this book is also aimed at financial market practitioners participating in capital market facing businesses who seek to keep abreast with and draw inspiration from novel approaches in market data analysis. The first two chapters of the book contains introductory material on stochastic analysis and the classical diffusion stock market models. The remaining chapters discuss more special stock and bond market models and special methods of pathwise inference for market parameter for different models. The final chapter describes applications of numerical methods of inference of bond market parameters to forecasting of short rate. Nikolai Dokuchaev is an associate professor in Mathematics and Statistics at Curtin University. His research interests include mathematical and statistical finance, stochastic analysis, PDEs, control, and signal processing. Lin Yee Hin is a practitioner in the capital market facing industry. His research interests include econometrics, non-parametric regression, and scientific computing.

Book Flattening the Volatility Smile

Download or read book Flattening the Volatility Smile written by Tom Arnold and published by . This book was released on 2002 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: By using an over-identified Generalized Method of Moments (GMM) estimation procedure with careful consideration for data biases existing in the previous literature, we estimate parameters for a stochastic volatility jump diffusion (SVJ) model. The estimated parameters indicate a statistically significant highly negative infrequent jump process in the underlying security return distribution consistent with market crashes. When comparing to a stochastic volatility (SV) option pricing model, the SVJ is more robust but not always the superior model. The robustness of the models is further gauged by evaluating the performance up to a year beyond the estimation data. Again, the SVJ model generally (but not always) performs better.stochastic volatility, jump diffusion.

Book On Probability Distributions of Diffusions and Financial Models with Non globally Smooth Coefficients

Download or read book On Probability Distributions of Diffusions and Financial Models with Non globally Smooth Coefficients written by Stefano De Marco and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some recent works in the field of mathematical finance have brought new light on the importance of studying the regularity and the tail asymptotics of distributions for certain classes of diffusions with non-globally smooth coefficients. In this Ph.D. dissertation we deal with some issues in this framework. In a first part, we study the existence, smoothness and space asymptotics of densities for the solutions of stochastic differential equations assuming only local conditions on the coefficients of the equation. Our analysis is based on Malliavin calculus tools and on « tube estimates » for Ito processes, namely estimates for the probability that the trajectory of an Ito process remains close to a deterministic curve. We obtain significant estimates of densities and distribution functions in general classes of option pricing models, including generalisations of CIR and CEV processes and Local-Stochastic Volatility models. In the latter case, the estimates we derive have an impact on the moment explosion of the underlying price and, consequently, on the large-strike behaviour of the implied volatility. Parametric implied volatility modeling, in its turn, makes the object of the second part. In particular, we focus on J. Gatheral's SVI model, first proposing an effective quasi-explicit calibration procedure and displaying its performances on market data. Then, we analyse the capability of SVI to generate efficient approximations of symmetric smiles, building an explicit time-dependent parameterization. We provide and test the numerical application to the Heston model (without and with displacement), for which we generate semi-closed expressions of the smile.

Book Stochastic volatility and the pricing of financial derivatives

Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Book Modeling And Pricing Of Swaps For Financial And Energy Markets With Stochastic Volatilities

Download or read book Modeling And Pricing Of Swaps For Financial And Energy Markets With Stochastic Volatilities written by Anatoliy Swishchuk and published by World Scientific. This book was released on 2013-06-03 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.