A Stochastic Volatility Model With Realized Measures For Option Pricing
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A Stochastic Volatility Model With Realized Measures For Option Pricing
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Author : Giacomo Bormetti
language : en
Publisher:
Release Date : 2019
A Stochastic Volatility Model With Realized Measures For Option Pricing written by Giacomo Bormetti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence - the crucial parameter in pricing Standard and Poor's 500 Index options.
Pricing Models Of Volatility Products And Exotic Variance Derivatives
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Author : Yue Kuen Kwok
language : en
Publisher: CRC Press
Release Date : 2022-05-08
Pricing Models Of Volatility Products And Exotic Variance Derivatives written by Yue Kuen Kwok and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-08 with Mathematics categories.
Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives
Assessing The Quality Of Volatility Estimators Via Option Pricing
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Author : Simona Sanfelici
language : en
Publisher:
Release Date : 2013
Assessing The Quality Of Volatility Estimators Via Option Pricing written by Simona Sanfelici and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
The aim of this paper is to measure and assess the accuracy of different volatility estimators based on high frequency data in an option pricing context. For this, we use a discrete-time stochastic volatility model based on Auto-Regressive-Gamma (ARG) dynamics for the volatility.First, ARG processes are presented both under historical and risk-neutral measure, in an affine stochastic discount factor framework. The model parameters are estimated exploiting the informative content of historical high frequency data. Secondly, option pricing is performed via Monte Carlo techniques. This framework allows us to measure the quality of different volatility estimators in terms of mispricing with respect to real option data, leaving to the ARG volatility model the role of a tool. Our analysis points out that using high frequency intra-day returns allows to obtain more accurate ex post estimation of the true (unobservable) return variation than do the more traditional sample variances based on daily returns, and this is reflected in the quality of pricing. Moreover, estimators robust to microstructure effects show an improvement over the realized volatility estimator. The empirical analysis is conducted on European options written on S&P500 index.
A Comparison Of Option Prices Under Different Pricing Measures In A Stochastic Volatility Model With Correlation
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Author : Vicky Henderson
language : en
Publisher:
Release Date : 2004
A Comparison Of Option Prices Under Different Pricing Measures In A Stochastic Volatility Model With Correlation written by Vicky Henderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk.As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.As a concrete example, we specialise to a variant of the Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q. Choice of quot;qquot; is shown to influence the level of the implied volatility smile for options of varying maturity.
Stochastic Volatility
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Author :
language : en
Publisher:
Release Date : 2009
Stochastic Volatility written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Options (Finance) categories.
"Given the importance of return volatility on a number of practical financial management decisions, the efforts to provide good real- time estimates and forecasts of current and future volatility have been extensive. The main framework used in this context involves stochastic volatility models. In a broad sense, this model class includes GARCH, but we focus on a narrower set of specifications in which volatility follows its own random process, as is common in models originating within financial economics. The distinguishing feature of these specifications is that volatility, being inherently unobservable and subject to independent random shocks, is not measurable with respect to observable information. In what follows, we refer to these models as genuine stochastic volatility models. Much modern asset pricing theory is built on continuous- time models. The natural concept of volatility within this setting is that of genuine stochastic volatility. For example, stochastic-volatility (jump- ) diffusions have provided a useful tool for a wide range of applications, including the pricing of options and other derivatives, the modeling of the term structure of risk-free interest rates, and the pricing of foreign currencies and defaultable bonds. The increased use of intraday transaction data for construction of so-called realized volatility measures provides additional impetus for considering genuine stochastic volatility models. As we demonstrate below, the realized volatility approach is closely associated with the continuous-time stochastic volatility framework of financial economics. There are some unique challenges in dealing with genuine stochastic volatility mode."--Federal Reserve Bank of Chicago.
Stochastic Volatility And Realized Stochastic Volatility Models
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Author : Makoto Takahashi
language : en
Publisher: Springer Nature
Release Date : 2023-04-18
Stochastic Volatility And Realized Stochastic Volatility Models written by Makoto Takahashi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-18 with Business & Economics categories.
This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.
Stochastic Volatility
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Author : Neil Shephard
language : en
Publisher: OUP Oxford
Release Date : 2005-03-10
Stochastic Volatility written by Neil Shephard and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-10 with Business & Economics categories.
Stochastic volatility is the main concept used in the fields of financial economics and mathematical finance to deal with time-varying volatility in financial markets. This book brings together some of the main papers that have influenced the field of the econometrics of stochastic volatility, and shows that the development of this subject has been highly multidisciplinary, with results drawn from financial economics, probability theory, and econometrics, blending to produce methods and models that have aided our understanding of the realistic pricing of options, efficient asset allocation, and accurate risk assessment. A lengthy introduction by the editor connects the papers with the literature.
Advanced Equity Derivatives
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Author : Sebastien Bossu
language : en
Publisher: John Wiley & Sons
Release Date : 2014-05-19
Advanced Equity Derivatives written by Sebastien Bossu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-19 with Business & Economics categories.
In Advanced Equity Derivatives: Volatility and Correlation, Sébastien Bossu reviews and explains the advanced concepts used for pricing and hedging equity exotic derivatives. Designed for financial modelers, option traders and sophisticated investors, the content covers the most important theoretical and practical extensions of the Black-Scholes model. Each chapter includes numerous illustrations and a short selection of problems, covering key topics such as implied volatility surface models, pricing with implied distributions, local volatility models, volatility derivatives, correlation measures, correlation trading, local correlation models and stochastic correlation. The author has a dual professional and academic background, making Advanced Equity Derivatives: Volatility and Correlation the perfect reference for quantitative researchers and mathematically savvy finance professionals looking to acquire an in-depth understanding of equity exotic derivatives pricing and hedging.
Stochastic Volatility Modeling
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Author : Lorenzo Bergomi
language : en
Publisher: CRC Press
Release Date : 2015-12-16
Stochastic Volatility Modeling written by Lorenzo Bergomi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-16 with Business & Economics categories.
Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Asymptotic Methods For Option Pricing In Finance
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Author : David Krief
language : en
Publisher:
Release Date : 2018
Asymptotic Methods For Option Pricing In Finance written by David Krief and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
In this thesis, we study several mathematical finance problems, related to the pricing of derivatives. Using different asymptotic approaches, we develop methods to calculate accurate approximations of the prices of certain types of options in cases where no explicit formulas are available.In the first chapter, we are interested in the pricing of path-dependent options, with Monte-Carlo methods, when the underlying is modelled as an affine stochastic volatility model. We prove a long-time trajectorial large deviations principle. We then combine it with Varadhan's Lemma to calculate an asymptotically optimal measure change, that allows to reduce significantly the variance of the Monte-Carlo estimator of option prices.The second chapter considers the pricing with Monte-Carlo methods of options that depend on several underlying assets, such as basket options, in the Wishart stochastic volatility model, that generalizes the Heston model. Following the approach of the first chapter, we prove that the process verifies a long-time large deviations principle, that we use to reduce significantly the variance of the Monte-Carlo estimator of option prices, through an asymptotically optimal measure change. In parallel, we use the large deviations property to characterize the long-time behaviour of the Black-Scholes implied volatility of basket options.In the third chapter, we study the pricing of options on realized variance, when the spot volatility is modelled as a diffusion process with constant volatility. We use recent asymptotic results on densities of hypo-elliptic diffusions to calculate an expansion of the density of realized variance, that we integrate to obtain an expansion of option prices and their Black-Scholes implied volatility.The last chapter is dedicated to the pricing of interest rate derivatives in the Levy Libor market model, that generaliszes the classical (log-normal) Libor market model by introducing jumps. Writing the first model as a perturbation of the second and using the Feynman-Kac representation, we calculate explicit expansions of the prices of interest rate derivatives and, in particular, caplets and swaptions.