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Download or read book Topics on Option Valuation and Model Calibration written by and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stefano M. Iacus
Publisher : John Wiley & Sons
ISBN 13 : 1119990203
Total Pages : 402 pages
Book Rating : 4.1/5 (199 download)
Download or read book Option Pricing and Estimation of Financial Models with R written by Stefano M. Iacus and published by John Wiley & Sons. This book was released on 2011-02-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.
Author : Janis Bauer
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (13 download)
Download or read book Model Calibration in Thinly Traded Derivatives Markets written by Janis Bauer and published by . This book was released on 2017 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Loss functions are widely used to calibrate option pricing models to cross-sectional derivatives quotes. However, these approaches come with the disadvantage that estimated model parameters often appear to lack stability over time. On small option markets, this sign of over-fitting is typically pronounced, in particular, when the number of traded options is small and bid-ask spreads are large. So far, there is only little academic literature addressing issues with over-fitting in the context of daily model calibration. In order to fill this gap, we implement a state-space system for the Heston and the PBS model that can be solved with Kalman filters. An empirical analysis using data from five different option markets suggests that Kalman filters are a promising alternative approach to prevent over-fitting, stabilize model parameters and Greeks, and improve the out-of-sample pricing performance on markets with low trading activity.
Author : Malcolm Kemp
Publisher : John Wiley & Sons
ISBN 13 : 0470684895
Total Pages : 647 pages
Book Rating : 4.4/5 (76 download)
Download or read book Market Consistency written by Malcolm Kemp and published by John Wiley & Sons. This book was released on 2009-09-10 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: Achieving market consistency can be challenging, even for the most established finance practitioners. In Market Consistency: Model Calibration in Imperfect Markets, leading expert Malcolm Kemp shows readers how they can best incorporate market consistency across all disciplines. Building on the author's experience as a practitioner, writer and speaker on the topic, the book explores how risk management and related disciplines might develop as fair valuation principles become more entrenched in finance and regulatory practice. This is the only text that clearly illustrates how to calibrate risk, pricing and portfolio construction models to a market consistent level, carefully explaining in a logical sequence when and how market consistency should be used, what it means for different financial disciplines and how it can be achieved for both liquid and illiquid positions. It explains why market consistency is intrinsically difficult to achieve with certainty in some types of activities, including computation of hedging parameters, and provides solutions to even the most complex problems. The book also shows how to best mark-to-market illiquid assets and liabilities and to incorporate these valuations into solvency and other types of financial analysis; it indicates how to define and identify risk-free interest rates, even when the creditworthiness of governments is no longer undoubted; and it explores when practitioners should focus most on market consistency and when their clients or employers might have less desire for such an emphasis. Finally, the book analyses the intrinsic role of regulation and risk management within different parts of the financial services industry, identifying how and why market consistency is key to these topics, and highlights why ideal regulatory solvency approaches for long term investors like insurers and pension funds may not be the same as for other financial market participants such as banks and asset managers.
Author : Craig A. Friedman
Publisher :
ISBN 13 :
Total Pages : 18 pages
Book Rating : 4.:/5 (13 download)
Download or read book Some Economically Meaningful Option Model Calibration Performance Measures written by Craig A. Friedman and published by . This book was released on 2014 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: The desire to more accurately calibrate option pricing models to liquid option prices has been an important driver of the growth of the option pricing literature and practice. However, the most commonly used model calibration accuracy metrics are not designed to reflect the economic consequences of trading based on model prices. To address this shortcoming, we derive, from first principles, in an idealized market setting, new, tractable, and economically meaningful, utility-based, measures of option pricing model calibration performance. We show that when pricing errors are “small,” our measures closely approximate popular percentage pricing error-based metrics. However, our measures can be quite different when model prices are smaller than they ought to be (which can happen when the option pricing model does not properly take into account fat-tailed asset return effects). We compare our measures with widely used metrics and show, via examples using SPX options data, that our new measures better inform us about the economic consequences of model pricing error and thereby better allow us to select among candidate option pricing models.
Author : Julien Guyon
Publisher : CRC Press
ISBN 13 : 1466570334
Total Pages : 486 pages
Book Rating : 4.4/5 (665 download)
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing Problems For nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research—including Risk magazine’s 2013 Quant of the Year—Nonlinear Option Pricing compares various numerical methods for solving high-dimensional nonlinear problems arising in option pricing. Designed for practitioners, it is the first authored book to discuss nonlinear Black-Scholes PDEs and compare the efficiency of many different methods. Real-World Solutions for Quantitative Analysts The book helps quants develop both their analytical and numerical expertise. It focuses on general mathematical tools rather than specific financial questions so that readers can easily use the tools to solve their own nonlinear problems. The authors build intuition through numerous real-world examples of numerical implementation. Although the focus is on ideas and numerical examples, the authors introduce relevant mathematical notions and important results and proofs. The book also covers several original approaches, including regression methods and dual methods for pricing chooser options, Monte Carlo approaches for pricing in the uncertain volatility model and the uncertain lapse and mortality model, the Markovian projection method and the particle method for calibrating local stochastic volatility models to market prices of vanilla options with/without stochastic interest rates, the a + bλ technique for building local correlation models that calibrate to market prices of vanilla options on a basket, and a new stochastic representation of nonlinear PDE solutions based on marked branching diffusions.
Author : Ingo Beyna
Publisher : Springer Science & Business Media
ISBN 13 : 3642349250
Total Pages : 220 pages
Book Rating : 4.6/5 (423 download)
Download or read book Interest Rate Derivatives written by Ingo Beyna and published by Springer Science & Business Media. This book was released on 2013-02-20 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of interest rate models introduced by O. Cheyette in 1994 is a subclass of the general HJM framework with a time dependent volatility parameterization. This book addresses the above mentioned class of interest rate models and concentrates on the calibration, valuation and sensitivity analysis in multifactor models. It derives analytical pricing formulas for bonds and caplets and applies several numerical valuation techniques in the class of Cheyette model, i.e. Monte Carlo simulation, characteristic functions and PDE valuation based on sparse grids. Finally it focuses on the sensitivity analysis of Cheyette models and derives Model- and Market Greeks. To the best of our knowledge, this sensitivity analysis of interest rate derivatives in the class of Cheyette models is unique in the literature. Up to now the valuation of interest rate derivatives using PDEs has been restricted to 3 dimensions only, since the computational effort was too great. The author picks up the sparse grid technique, adjusts it slightly and can solve high-dimensional PDEs (four dimensions plus time) accurately in reasonable time. Many topics investigated in this book are new areas of research and make a significant contribution to the scientific community of financial engineers. They also represent a valuable development for practitioners.
Author : Robert A. Jarrow
Publisher :
ISBN 13 :
Total Pages : 39 pages
Book Rating : 4.:/5 (13 download)
Download or read book Specification Tests of Calibrated Option Pricing Models written by Robert A. Jarrow and published by . This book was released on 2013 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of the popularity of model calibration in finance, empirical researchers have put more emphasis on model estimation than on the equally important goodness-of-fit problem. This is due partly to the ignorance of modelers, and more to the ability of existing statistical tests to detect specification errors. In practice, models are often calibrated by minimizing the sum of squared difference between the modelled and actual observations. It is challenging to disentangle model error from estimation error in the residual series. To circumvent the difficulty, we study an alternative way of estimating the model by exact calibration. We argue that standard time series tests based on the exact approach can better reveal model misspecifications than the error minimizing approach. In the context of option pricing, we illustrate the usefulness of exact calibration in detecting model misspecification. Under heteroskedastic observation error structure, our simulation results shows that the Black-Scholes model calibrated by exact approach delivers more accurate hedging performance than that calibrated by error minimization.
Author : Simona Sanfelici
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (13 download)
Download or read book Calibration of a Nonlinear Feedback Option Pricing Model written by Simona Sanfelici and published by . This book was released on 2013 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider an option pricing model proposed by, where the implementation of dynamic hedging strategies has a feedback impact on the price process of the underlying asset. We present numerical results showing that the smile and skewness patterns of implied volatility can actually be reproduced as a consequence of dynamical hedging. The simulations are performed using a suitable semi-implicit finite difference method.Moreover, we perform a calibration of the nonlinear model to market data and we compare it with more popular models, such as the Black-Scholes formula, the Jump-Diffusion model and Heston's model. In judging the alternative models, we consider the following issues: (i) the consistency of the implied structural parameters with the times-series data; (ii) out-of-sample pricing; (iii) parameter uniformity across different moneyness and maturity classes. Overall, nonlinear feedback due to hedging strategies can, at least in part, contribute to explain from a theoretical and quantitative point of view the strong pricing biases of the Black-Scholes formula, although stochastic volatility effects are more important in this regard.
Author : Cristian Homescu
Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (13 download)
Download or read book Local Stochastic Volatility Models written by Cristian Homescu and published by . This book was released on 2014 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze in detail calibration and pricing performed within the framework of local stochastic volatility LSV models, which have become the industry market standard for FX and equity markets. We present the main arguments for the need of having such models, and address the question whether jumps have to be included. We include a comprehensive literature overview, and focus our exposition on important details related to calibration procedures and option pricing using PDEs or PIDEs derived from LSV models. We describe calibration procedures, with special attention given to usage and solution of corresponding forward Kolmogorov PDE/PIDE, and outline powerful algorithms for estimation of model parameters. Emphasis is placed on presenting practical details regarding the setup and the numerical solution of both forward and backward PDEs/PIDEs obtained from the LSV models. Consequently we discuss specifics (based on our experience and best practices from literature) regarding choice of boundary conditions, construction of nonuniform spatial grids and adaptive temporal grids, selection of efficient and appropriate finite difference schemes (with possible enhancements), etc. We also show how to practically integrate specific features of various types of financial instruments within calibration and pricing settings. We consider all questions and topics identified as most relevant during the selection, calibration and pricing procedures associated with local stochastic volatility models, providing answers (to the best of our knowledge), and present references for deeper understanding and for additional perspectives. In a nutshell, it is our intention to present here an effective roadmap for a successful LSV journey.
Author : Stefanie Hasse
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (781 download)
Download or read book Local Vs. Global Calibration - A Comparison of Option Hedging Strategies and Option Pricing Models written by Stefanie Hasse and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the empirical relationship of model fit, calibration methods and hedging performance for individual equity options. The sample used comprises of about 76,000 option prices for individual equity options recorded between January 2, 2008 and December 31, 2009. This sample has been used to first calibrate the stochastic volatility model by Heston (1993) by using two different calibration techniques, local and global calibration, and then to investigate hedging performance of the Heston model versus three simple adjustments to the model by Black and Scholes (1973) (BSM). It is found that the sticky-strike adjustment to the BSM outperforms the Heston model for delta and delta-gamma hedging of individual equity options, and the Heston model using parameters from local calibration performs best for delta-vega hedges. The results apply to both daily and weekly rebalancing of the hedging portfolios and are robust with respect to different moneyness categories and market regimes.
Author : Andrey Itkin
Publisher : World Scientific
ISBN 13 : 9811212783
Total Pages : 205 pages
Book Rating : 4.8/5 (112 download)
Download or read book Fitting Local Volatility: Analytic And Numerical Approaches In Black-scholes And Local Variance Gamma Models written by Andrey Itkin and published by World Scientific. This book was released on 2020-01-22 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black-Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.This book was written with the purpose of presenting new results previously developed in a series of papers and explaining them consistently, starting from the general concept of Dupire, Derman and Kani and then concentrating on various extensions proposed by the author and his co-authors. This volume collects all the results in one place, and provides some typical examples of the problems that can be efficiently solved using the proposed methods. This also results in a faster calibration of the local and implied volatility surfaces as compared to standard approaches.The methods and solutions presented in this volume are new and recently published, and are accompanied by various additional comments and considerations. Since from the mathematical point of view, the level of details is closer to the applied rather than to the abstract or pure theoretical mathematics, the book could also be recommended to graduate students with majors in computational or quantitative finance, financial engineering or even applied mathematics. In particular, the author used to teach some topics of this book as a part of his special course on computational finance at the Tandon School of Engineering, New York University.
Author : Yoshio Miyahara
Publisher : World Scientific
ISBN 13 : 1848163487
Total Pages : 200 pages
Book Rating : 4.8/5 (481 download)
Download or read book Option Pricing in Incomplete Markets written by Yoshio Miyahara and published by World Scientific. This book was released on 2012 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers the reader practical methods to compute the option prices in the incomplete asset markets. The [GLP & MEMM] pricing models are clearly introduced, and the properties of these models are discussed in great detail. It is shown that the geometric L(r)vy process (GLP) is a typical example of the incomplete market, and that the MEMM (minimal entropy martingale measure) is an extremely powerful pricing measure. This volume also presents the calibration procedure of the [GLP \& MEMM] model that has been widely used in the application of practical problem
Author : Jianwei Zhu
Publisher : Springer Science & Business Media
ISBN 13 : 3642018084
Total Pages : 338 pages
Book Rating : 4.6/5 (42 download)
Download or read book Applications of Fourier Transform to Smile Modeling written by Jianwei Zhu and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy ́ jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene?t from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory.
Author : Emlyn James Flint
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (13 download)
Download or read book Fractional Black-Scholes Option Pricing, Volatility Calibration and Implied Hurst Exponents written by Emlyn James Flint and published by . This book was released on 2017 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper addresses several theoretical and practical issues in option pricing and implied volatility calibration in a fractional Black-Scholes market. In particular, we discuss how the fractional Black-Scholes model admits a non-constant implied volatility term structure when the Hurst exponent is not 0.5, and also that one-year implied volatility is independent of Hurst exponent and equivalent to fractional volatility. Building on these observations, we introduce a novel 8-parameter fractional Black-Scholes inspired, or FBSI, model. This deterministic volatility surface model is based on the fractional Black-Scholes framework and uses Gatheral's (2004) SVI pamaterisation for the fractional volatility skew and a quadratic parameterisation for the Hurst exponent skew. The issue of arbitrage-free calibration for the FBSI model is addressed in depth and it is proven in general that any FBSI volatility surface will be free from calendar-spread arbitrage. The FBSI model is empirically tested on implied volatility data on a South African equity index as well as the USDZAR exchange rate. Results show that the FBSI model fits the equity index implied volatility data very well and that a more flexible Hurst exponent parameterisation is needed to accurately fit the USDZAR implied volatility surface data.
Author : Michael Weber
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (13 download)
Download or read book American Option Valuation written by Michael Weber and published by . This book was released on 2017 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article analyzes the issue of American option valuation when the underlying exhibits a GARCH-type volatility process. We propose the usage of Rubinstein's Edgeworth binomial tree (EBT) in contrast to simulation-based methods being considered in previous studies. The EBT-based valuation approach makes an implied calibration of the pricing model feasible. By empirically analyzing the pricing performance of American index and equity options, we illustrate the superiority of the proposed approach.
Author : Juho Kanniainen
Publisher :
ISBN 13 :
Total Pages : 6 pages
Book Rating : 4.:/5 (13 download)
Download or read book Distributed Calibration of Option Pricing Models with Multiple Contracts Written on Different Underlying Assets written by Juho Kanniainen and published by . This book was released on 2017 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: Think about a situation, where a financial institution has multiple option positions, each written on a different underlying asset, and the unexpected arrival of market-wide news shakes the markets. In the case of such a market-wide news arrival, all the volatility models on different underlyings must be immediately re-calibrated for robust option pricing and hedging. Unfortunately, the calibration of models using data on multiple underlying securities can take too long, especially, if advanced non-affine models without analytical solutions are used. This work demonstrates how multiple independent calibration tasks (on different underlyings) can be efficiently accelerated by Techila, reducing the length of the wall-clock computation time from 7 hours to a few minutes.
