Download or read book Option Valuation Under Stochastic Volatility written by Alan L. Lewis and published by . This book was released on 2000 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing Under Stochastic Volatility Model written by Hak Min Lim and published by . This book was released on 2003 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Application of Stochastic Volatility Models in Option Pricing written by Pascal Debus and published by GRIN Verlag. This book was released on 2013-09-09 with total page 59 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bachelorarbeit aus dem Jahr 2010 im Fachbereich BWL - Investition und Finanzierung, Note: 1,2, EBS Universität für Wirtschaft und Recht, Sprache: Deutsch, Abstract: The Black-Scholes (or Black-Scholes-Merton) Model has become the standard model for the pricing of options and can surely be seen as one of the main reasons for the growth of the derivative market after the model ́s introduction in 1973. As a consequence, the inventors of the model, Robert Merton, Myron Scholes, and without doubt also Fischer Black, if he had not died in 1995, were awarded the Nobel prize for economics in 1997. The model, however, makes some strict assumptions that must hold true for accurate pricing of an option. The most important one is constant volatility, whereas empirical evidence shows that volatility is heteroscedastic. This leads to increased mispricing of options especially in the case of out of the money options as well as to a phenomenon known as volatility smile. As a consequence, researchers introduced various approaches to expand the model by allowing the volatility to be non-constant and to follow a sto-chastic process. It is the objective of this thesis to investigate if the pricing accuracy of the Black-Scholes model can be significantly improved by applying a stochastic volatility model.

Download or read book Option Valuation Under Stochastic Volatility II written by Alan L. Lewis and published by . This book was released on 2016-05-12 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the author's well-received "Option Valuation under Stochastic Volatility." It extends that work to jump-diffusions and many related topics in quantitative finance. Topics include spectral theory for jump-diffusions, boundary behavior for short-term interest rate models, modelling VIX options, inference theory, discrete dividends, and more. It provides approximately 750 pages of original research in 26 chapters, with 165 illustrations, Mathematica, and some C/C++ codes. The first 12 chapters (550 pages) are completely new. Also included are reprints of selected previous publications of the author for convenient reference. The book should interest both researchers and quantitatively-oriented investors and traders. First 12 chapters: Slow Reflection, Jump-Returns, & Short-term Interest Rates Spectral Theory for Jump-diffusions Joint Time Series Modelling of SPX and VIX Modelling VIX Options (and Futures) under Stochastic Volatility Stochastic Volatility as a Hidden Markov Model Continuous-time Inference: Mathematical Methods and Worked Examples A Closer Look at the Square-root and 3/2-model A Closer Look at the SABR Model Back to Basics: An Update on the Discrete Dividend Problem PDE Numerics without the Pain Exact Solution to Double Barrier Problems under a Class of Processes Advanced Smile Asymptotics: Geometry, Geodesics, and All That

Download or read book American Option Pricing Under Stochastic Volatility written by Manisha Goswami and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The approximate method to price American options makes use of the fact that accurate pricing of these options does not require exact determination of the early exercise boundary. Thus, the procedure mixes the two models of constant and stochastic volatility. The idea is to obtain early exercise boundary through constant volatility model using the approximation methods of AitSahlia and Lai or Ju and then utilize this boundary to price the options under stochastic volatility models. The data on S & P 100 Index American options is used to analyze the pricing performance of the mixing of the two models. The performance is studied with respect to percentage pricing error and absolute pricing errors for each money-ness maturity group.

Download or read book Option Pricing Under Stochastic Volatility written by Martin Jan Andersen and published by . This book was released on 2015 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book American Options Under Stochastic Volatility written by Arun Chockalingam and published by . This book was released on 2012 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of pricing an American option written on an underlying asset with constant price volatility has been studied extensively in literature. Real-world data, however, demonstrates that volatility is not constant and stochastic volatility models are used to account for dynamic volatility changes. Option pricing methods that have been developed in literature for pricing under stochastic volatility focus mostly on European options. We consider the problem of pricing American options under stochastic volatility which has relatively had much less attention from literature. First, we develop an exercise-policy improvement procedure to compute the optimal exercise policy and option price. We show that the scheme monotonically converges for various popular stochastic volatility models in literature. Second, using this computational tool, we explore a variety of questions that seek insights into the dependence of option prices, exercise policies and implied volatilities on the market price of volatility risk and correlation between the asset and stochastic volatility.

Download or read book Option Pricing Under Stochastic Volatility written by Dimitrios Gkamas and published by . This book was released on 2002 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing Under Stochastic Volatility and Trading Volume written by Sadayuki Ono and published by . This book was released on 2005 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a pricing formula for European options that is derived from a model in which changes in the underlying price and trading volumes are jointly determined by exogenous events. The joint determination of volume and price changes provides a crucial link between volatility of the price process and an observable variable. The model works as follows: the process of information arrival (news) is taken to be a point process that induces simultaneous jumps in price and trading volume. In addition, price has a diffusion component that corresponds to background noise, and the parameter that governs the volatility of this component is a continuously weighted average of past trading volume. This specification makes increments to the volatility process depend on the current level of volatility and news and thereby accounts for the observed persistence in volatility. Moreover, it makes volatility an observable instead of a latent variable, as it is in the usual stochastic volatility setups. Options can be priced as in the Heston framework by inverting the conditional characteristic function of underlying price at expiration. We find that the model accounts well for time varying volatility smiles and term structures and that out-of-sample price forecasts for a sample of stock options are superior not only to those of standard stochastic volatility models but even to the benchmark ad hoc procedure of plugging current implicit volatilities into the Black-Scholes formula.

Download or read book A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation written by Vicky Henderson and published by . This book was released on 2004 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Array RQMC for Option Pricing Under Stochastic Volatility Models written by Amal Ben Abdellah and published by . This book was released on 2019 with total page 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 Option Pricing Under Stochastic Volatility written by Josep Perelló and published by . This book was released on 2014 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbeck subordinated process describing the randomness of the log-volatility. We derive an approximate option price that is valid when (i) the fluctuations of the volatility are larger than its normal level, (ii) the volatility presents a slow driving force toward its normal level and, finally, (iii) the market price of risk is a linear function of the log-volatility. We study the resulting European call price and its implied volatility for a range of parameters consistent with daily Dow Jones Index data.

Download or read book Binomial Option Pricing Under Stochastic Volatility and Correlated State Variables written by Jimmy E. Hilliard and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article develops a method for valuing contingent payoffs for a non-constant volatility process via a simple recombining binomial tree. The direct application of the technology provides a way to price, for example, American calls or puts governed by a stock price process with stochastic volatility. The stock price and volatility diffusions may have non-zero correlations. This feature allows model prices consistent with the volatility smile. Numerical estimates of the hedge statistics (delta, gamma, and vega) are obtained directly from the tree.

Download or read book Pricing Options Under Heston s Stochastic Volatility Model Via Accelerated Explicit Finite Differencing Methods written by Conall O'Sullivan and published by . This book was released on 2010 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present an acceleration technique, effective for explicit finite difference schemes describing diffusive processes with nearly symmetric operators, called Super-Time-Stepping (STS). The technique is applied to the two-factor problem of option pricing under stochastic volatility. It is shown to significantly reduce the severity of the stability constraint known as the Courant-Friedrichs-Lewy condition whilst retaining the simplicity of the chosen underlying explicit method. For European and American put options under Heston's stochastic volatility model we demonstrate degrees of acceleration over standard explicit methods sufficient to achieve comparable, or superior, efficiencies to a benchmark implicit scheme. We conclude that STS is a powerful tool for the numerical pricing of options and propose them as the method-of-choice for exotic financial instruments in two and multi-factor models.

Download or read book Multiscale Stochastic Volatility for Equity Interest Rate and Credit Derivatives written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2011-09-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.