Download or read book Option Hedging and Parameter Estimation when Volatility is Stochastic written by Jason Douglas Fink and published by . This book was released on 2002 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Estimation of a Stochastic Volatility Model Using Pricing and Hedging Information written by Jason Fink and published by . This book was released on 2005 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: Estimation of option pricing models in which the underlying asset exhibits stochastic volatility presents complicated econometric questions. One such question, thus far unstudied, is whether the inclusion of information derived from hedging relationships implied by an option pricing model may be used in conjunction with pricing information to provide more reliable parameter estimates than the use of pricing information alone. This paper estimates, using a simple least-squares procedure, the stochastic volatility model of Heston (1993), and includes hedging information in the objective function. This hedging information enters the objective function through a weighting parameter that is chosen optimally within the model. With the weight appropriately chosen, we find that incorporating the hedging information reduces both the out-of-sample hedging and pricing errors associated with the Heston model.

Download or read book Volatility Surface and Term Structure written by Kin Keung Lai and published by Routledge. This book was released on 2013-09-11 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.

Download or read book Pricing and Hedging Index Options Under Stochastic Volatility written by Saikat Nandi and published by . This book was released on 1996 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hedging Options in the Incomplete Market with Stochastic Volatility written by Rituparna Sen and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We show that it is possible to avoid the discrepancies of continuous path models for stock prices and still be able to hedge options if one models the stock price process as a birth and death process. One needs the stock and another market traded derivative to hedge an option in this setting. However, unlike in continuous models, number of extra traded derivatives required for hedging does not increase when the intensity process is stochastic. We obtain parameter estimates using Generalized Method of Moments and describe the Monte Carlo algorithm to obtain option prices. We show that one needs to use filtering equations for inference in the stochastic intensity setting. We present real data applications to study the performance of our modeling and estimation techniques.

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 Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Download or read book A Mean Reverting Stochastic Volatility Option Pricing Model with an Analytic Solution written by Henrik Andersson and published by . This book was released on 2002 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we derive a closed form approximation to a stochastic volatility option-pricing model and propose a variant of EGARCH for parameter estimation. The model thereby provides a consistent approach to the problem of option pricing and parameter estimation. Using Swedish stocks, the model provides a good fit to the heteroscedasticity prevalent in the time-series. The stochastic volatility model also prices options on the underlying stock more accurately than the traditional Black-Scholes formula. This result holds for both historic and implied volatility. A large part of the volatility smile that is observed for options of different maturity and exercise prices is thereby explained.

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:

Download or read book Hedging Options in a GARCH Environment written by Robert F. Engle and published by . This book was released on 1994 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a methodology for testing the term structure of volatility forecasts derived from stochastic volatility models, and implements it to analyze models of S & P 500 index volatility. Volatility models are compared by their ability to hedge options positions sensitive to the term structure of volatility. Overall, the most effective hedge is a Black-Scholes (BS) delta-gamma hedge, while the BS delta-vega hedge is the least effective. The most successful volatility hedge is GARCH components delta-gamma, suggesting that the GARCH components estimate of the term structure of volatility is most accurate. The success of the BS delta-gamma hedge may be due to mispricing in the options market over the sample period.

Download or read book Improving Volatility Estimation and Options Hedging written by and published by . This book was released on 2001 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

Download or read book Option Hedging and Valuation Under Stochastic Volatility written by Joshua Rosenberg and published by . This book was released on 1996 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Volatility Models written by Jian Yang and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Derivatives in Financial Markets with Stochastic Volatility written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2000-07-03 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.

Download or read book Semiparametric Modeling of Implied Volatility written by Matthias R. Fengler and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers recent advances in the theory of implied volatility and refined semiparametric estimation strategies and dimension reduction methods for functional surfaces. The first part is devoted to smile-consistent pricing approaches. The second part covers estimation techniques that are natural candidates to meet the challenges in implied volatility surfaces. Empirical investigations, simulations, and pictures illustrate the concepts.

Download or read book Complex Systems in Finance and Econometrics written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.