Download or read book Option Pricing with Anomalous Scaling and Infinite State Switching Volatility written by Fulvio Baldovin and published by . This book was released on 2013 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volatility clustering, long-range dependence, non-Gaussianity and anomalous scaling are all well-known stylized facts of financial assets return dynamics. These elements have a relevant impact on the aptness of models for the pricing of options written on financial assets. We make us of a model developed in physics that captures the previously cited returns features. The model allows deriving closed form equations for option pricing. We present the model providing a financial interpretation of its components and discuss the parameters estimation. We then derive pricing equations and use them in an empirical application based on a major equity index option dataset.

Download or read book Option Pricing with Unobserved and Regime Switching Volatility written by Sean D. Campbell and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we use a regime-switching process to model the unobserved volatility of the underlying asset and derive a closed-form, risk-neutral option pricing formula. Specifically, our model implies the state price density (SPD) is a time-varying mixture of normals which can provide for time-varying excess kurtosis and skewness as agents learn about the state of volatility from realized returns. Furthermore, we show that our model generates the kinds of volatility quot;smilesquot; commonly found in option markets. We apply our two and three regime models to weekly Samp;P 500 option data and find our model fits the data better than other popular pricing models. Additionally, we find evidence that stock returns can be well-described by a markov switching framework with a very persistent low volatility regime followed by a less persistent moderate volatility regime and a highly non-persistent crash regime. Our estimation results don't suffer the so called quot;Peso Problemquot; as they come from option prices instead of the observed stock returns.

Download or read book Option Pricing Under Regime Switching analytical PDE and FFT Methods written by Mohammad Yousef Akhavein Sohrabi and published by . This book was released on 2011 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples.

Download or read book Option Volatility Pricing Advanced Trading Strategies and Techniques written by Sheldon Natenberg and published by McGraw Hill Professional. This book was released on 1994-08 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough discussion of volatility, the most important aspect of options trading. Shows how to identify mispriced options and to construct volatility and "delta neutral" spreads.

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

Download or read book Investigating the Market Price of Volatility Risk for Options in a Regime Switching Market written by Melissa Mielkie and published by . This book was released on 2013 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: To bridge the gap between the output of theoretical option pricing models and observed option prices on exchanges, it is necessary to price the volatility risk inherent in financial markets. Non zero market risk premia have been found in previous financial literature through an exploration of market data, quantifying the relationship between implied and realized volatility. Building upon previous work by Mielkie and Davison (2013) where an approximate solution was derived for options written on underlying assets with regime-switching volatility, we analyze the impact of the market price of volatility risk on theoretical option prices. Using financially intuitive constraints, we prove the necessity of placing restrictions on the market prices of volatility risk in order to get reasonable option prices. In particular, we show that negative state-dependent market prices of volatility risk are necessary in order for the option prices and corresponding hedge ratios to be financially rational. An exploration of the regime-switching option prices and their implied volatilities is given, as well as numerical results and intuition supporting our mathematical proofs.

Download or read book Option Pricing with Stochastic Volatility Following a Finite Markov Chain written by Chen Guo and published by . This book was released on 1996 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Preference free Option Pricing with Path dependent Volatility written by Steven L. Heston and published by . This book was released on 1998 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing with Continuous time Markov Chain Regime Switching written by Craig Steven Edwards and published by . This book was released on 2004 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing with Long Memory Stochastic Volatility Models written by Zhigang Tong and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance.

Download or read book Option Pricing and Volatility written by and published by . This book was released on 2008 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Methods for American Option Pricing with Nonlinear Volatility written by Wen Wang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is organized as follows: Chapter 1 is an introduction to option pricing theory; Chapter 2 focuses on theoretical model of uncertain volatility; Chapter 3 introduces the numerical methods; Chapter 4 shows the experiment results; Chapter 5 summarizes the work and points out some future research directions.

Download or read book Option Volatility Pricing written by Sheldon Natenberg and published by . This book was released on 1994 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Option Pricing with Long Memory Stochastic Volatility Models written by Zhigang Tong and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we propose two continuous time stochastic volatility models with long memory that generalize two existing models. More importantly, we provide analytical formulae that allow us to study option prices numerically, rather than by means of simulation. We are not aware about analytical results in continuous time long memory case. In both models, we allow for the non-zero correlation between the stochastic volatility and stock price processes. We numerically study the effects of long memory on the option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter in short memory models. We also find that long memory models have the potential to accommodate the short term options and the decay of volatility skew better than the corresponding short memory stochastic volatility models.

Download or read book High Order Compact Finite Difference Scheme for Option Pricing in Stochastic Volatility Jump Models written by Bertram Düring and published by . This book was released on 2017 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility jump models, e.g. in Bates model. In such models the option price is determined as the solution of a partial integro-differential equation. The scheme is fourth order accurate in space and second order accurate in time. Numerical experiments for the European option pricing problem are presented. We validate the stability of the scheme numerically and compare its efficiency and hedging performance to standard finite difference methods. The new scheme outperforms a standard discretisation based on a second-order central finite difference approximation in all our experiments. At the same time, it is very efficient, requiring only one initial LU-factorisation of a sparse matrix to perform the option price valuation. It can also be useful to upgrade existing implementations based on standard finite differences in a straightforward manner to obtain a highly efficient option pricing code.

Download or read book Pricing American Options in Regime Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pricing problem for American options in Markov-modulated Lévy models is solved. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization procedure for regime-switching models. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. In contrast with the earlier version of the method, an explicit algorithm is formulated for wide classes of Lévy processes, and FFT and iFFT are used.

Download or read book Option Volatility and Pricing Strategies written by Sheldon Natenberg and published by . This book was released on 1994 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: