Download or read book Stochastic Volatility and Jump Diffusion Option Pricing Model written by Aytekin Sari and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Option Pricing for a Stochastic volatility Jump diffusion Model written by Guoqing Yan and published by . This book was released on 2006 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the accurate and fast European option pricing formulas, we calibrate the models to S&P 500 Index option quotes by least squares method. Spot variance and structural parameters for different models including Black-Scholes, Stochastic-Volatility. SVJD-Uniform, SVJD-Normal, SVJD-DbExp are estimated. Fitting performance of different models are compared and our proposed SVJD-Uniform model is found to fit the market data the best.
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 Exact and Approximated Option Pricing in a Stochastic Volatility Jump Diffusion Model written by Fernanda D'Ippoliti and published by . This book was released on 2014 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a stochastic volatility jump-diffusion model for option pricing with contemporaneous jumps in both spot return and volatility dynamics. The model admits, in the spirit of Heston, a closed-form solution for European-style options. To evaluate more complex derivatives for which there is no explicit pricing expression, such as barrier options, a numerical methodology, based on an “exact algorithm” proposed by Broadie and Kaya, is applied. This technique is called exact as no discretisation of dynamics is required. We end up testing the goodness of our methodology using, as real data, prices and implied volatilities from the DJ Euro Stoxx 50 market and providing some numerical results for barrier options and their Greeks.
Download or read book Numerical Analysis Of Stochastic Volatility Jump Diffusion Models written by Abdelilah Jraifi and published by LAP Lambert Academic Publishing. This book was released on 2014-06-30 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern economic world, the options contracts are used because they allow to hedge against the vagaries and risks refers to fluctuations in the prices of the underlying assets. The determination of the price of these contracts is of great importance for investors.We are interested in problems of options pricing, actually the European and Quanto options on a financial asset. The price of that asset is modeled by a multi-dimentional jump diffusion with stochastic volatility. Otherwise, the first model considers the volatility as a continuous process and the second model considers it as a jump process. Finally in the 3rd model, the underlying asset is without jump and volatility follows a model CEV without jump. This model allow better to take into account some phenomena observed in the markets. We develop numerical methods that determine the values of prices for these options. We first write the model as an integro-differential stochastic equations system "EIDS," of which we study existence and unicity of solutions. Then we relate the resolution of PIDE to the computation of the option value.
Download or read book High order Compact Finite Difference Schemes for Option Pricing in Stochastic Volatility Jump diffusion Models written by Alexander Pitkin and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Empirical Analysis of Jump Diffusion Stochastic Volatility Models for Currency Option Pricing written by Lei Zhang and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pricing European Style Options Under Jump Diffusion Processes with Stochastic Volatility written by Artur Sepp and published by . This book was released on 2014 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper surveys the developments in the finance literature with respect to applying the Fourier transform for option pricing under affine jump-diffusions. We provide a broad description of the issues and a detailed summary of the main points and features of the models proposed. First, we consider a wide class of affine jump-diffusions proposed for the asset price dynamics: jump-diffusions, diffusions with stochastic volatility, jump-diffusions with stochastic volatility, and jump-diffusions with stochastic volatility and jump intensity. Next we apply the Fourier transform for solving the problem of European option pricing under these price processes. We present two solution methods: the characteristic formula and the Black-Scholes-style formula. Finally, we discuss numerical implementation of pricing formulas and apply the considered processes for modeling the DAX options volatility surface.
Download or read book Jumps and Stochastic Volatility written by David S. Bates and published by . This book was released on 1993 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: An efficient method is developed for pricing American options on combination stochastic volatility/jump-diffusion processes when jump risk and volatility risk are systematic and nondiversifiable, thereby nesting two major option pricing models. The parameters implicit in PHLX-traded Deutschemark options of the stochastic volatility/jump- diffusion model and various submodels are estimated over 1984-91, and are tested for consistency with the $/DM futures process and the implicit volatility sample path. The parameters implicit in options are found to be inconsistent with the time series properties of implicit volatilities, but qualitatively consistent with log- differenced futures prices. No economically significant implicit expectations of exchange rate jumps were found in full-sample estimation, which is consistent with the reduced leptokurtosis of $/DM weekly exchange rate changes over 1984-91 relative to earlier periods.
Download or read book Essays on Empirical Performance of Affine Jump diffusion Option Pricing Models written by Xiang Zhang and published by . This book was released on 2012 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient Asian Option Pricing Under Regime Switching Jump Diffusions and Stochastic Volatility Models written by Justin Kirkby and published by . This book was released on 2020 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: Utilizing frame duality and a FFT-based implementation of density projection we develop a novel and efficient transform method to price Asian options for very general asset dynamics, including regime switching Levy processes and other jump diffusions as well as stochastic volatility models with jumps. The method combines Continuous-Time Markov Chain (CTMC) approximation, with Fourier pricing techniques. In particular, our method encompasses Heston, Hull-White, Stein-Stein, 3/2 model as well as recently proposed Jacobi, alpha-Hypergeometric, and 4/2 models, for virtually any type of jump amplitude distribution in the return process. This framework thus provides a unified approach to pricing Asian options in stochastic jump diffusion models and is readily extended to alternative exotic contracts. We also derive a characteristic function recursion by generalizing the Carverhill-Clewlow factorization which enables the application of transform methods in general. Numerical results are provided to illustrate the effectiveness of the method. Various extensions of this method have since been developed, including the pricing of barrier, American, and realized variance derivatives.
Download or read book Finite Activity Jump Models for Option Pricing written by Mercy Muthoni Koimburi and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is thesis aims to look at option pricing under affine jump diffusion processes, with particular emphasis on using Fourier transforms. The focus of the thesis is on using Fourier transform to price European options and Barrier options under the Heston stochastic volatility model and the Bates model. Bates model combines Merton's jump diffusion model and Heston's stochastic volatility model. We look at the calibration problem and use Matlab functions to model the DAX options volatility surface. Finally, using the parameters generated, we use the two stated models to price barrier options.
Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic
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 Pricing Stock Options in a Jump diffusion Model with Stochastic Volatility and Interest Rates written by Louis O. Scott and published by . This book was released on 1995 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Modeling and Analysis of Options with Jump diffusion Volatility written by Irena Andreevska and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: Several existing pricing models of financial derivatives as well as the effects of volatility risk are analyzed. A new option pricing model is proposed which assumes that stock price follows a diffusion process with square-root stochastic volatility. The volatility itself is mean-reverting and driven by both diffusion and compound Poisson process. These assumptions better reflect the randomness and the jumps that are readily apparent when the historical volatility data of any risky asset is graphed. The European option price is modeled by a homogeneous linear second-order partial differential equation with variable coefficients. The case of underlying assets that pay continuous dividends is considered and implemented in the model, which gives the capability of extending the results to American options. An American option price model is derived and given by a non-homogeneous linear second order partial integro-differential equation. Using Fourier and Laplace transforms an exact closed-form solution for the price formula for European call/put options is obtained.
Download or read book An Examination on the Roles of Diffusions and Stochastic Volatility in the Exponential Levy Jumps Models written by Elton Daal and published by . This book was released on 2006 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent studies have shown that stochastic volatility in a continuous-time framework provides an excellent fit for financial asset returns when combined with finite-activity Merton's type compound Poisson Jump-diffusion models. However, we demonstrate that stochastic volatility does not play a central role when incorporated with infinite-activity Leacute;vy type pure jump models such as variance-gamma and normal inverse Gaussian processes to model high and low frequency historical time-series SP500 index returns. In addition, whether sources of stochastic volatility are diffusions or jumps are not relevant to improve the overall empirical fits of returns. Nevertheless, stochastic diffusion volatility with infinite-activity Levy jumps processes considerably reduces SP500 index call option in-sample and out-of-sample pricing errors of long-term ATM and OTM options, which contributed to a substantial improvement of pricing performances of SVJ and EVGSV models, compared to constant volatility Levy-type pure jumps models and/or stochastic volatility model without jumps. Interestingly, unlike asset returns, whether pure Levy jumps specifications are finite or infinite activity is not an important factor to enhance option pricing model performances once stochastic volatility is incorporated. Option prices are computed via improved Fast Fourier Transform algorithm using characteristic functions to match arbitrary log-strike grids with equal intervals with each moneyness and maturity of actual market option prices considered in this paper.
