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 American Options in Levy Models with Stochastic Volatility written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in the sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of a Levy process with the intensity coefficient driven by the square root process with embedded jumps is derived. Numerical examples corroborate the general result about a gap between strike and early exercise boundary at expiry, in a neighborhood of r=0, in the presence of jumps.
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 Stochastic Modeling of Stock Prices Incorporating Jump Diffusion and Shot Noise Models written by Daniel Janocha and published by GRIN Verlag. This book was released on 2016-08-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: Master's Thesis from the year 2016 in the subject Mathematics - Stochastics, grade: 1,7, Technical University of Darmstadt (Forschungsgebiet Stochastik), course: Mathematik - Finanzmathematik, language: English, abstract: In this thesis, we present a stochastic model for stock prices incorporating jump diffusion and shot noise models based on the work of Altmann, Schmidt and Stute ("A Shot Noise Model For Financial Assets") and on its continuation by Schmidt and Stute ("Shot noise processes and the minimal martingale measure"). These papers differ in modeling the decay of the jump effect: Whereas it is deterministic in the first paper, it is stochastic in the last paper. In general, jump effects exist because of overreaction due to news in the press, due to illiquidity or due to incomplete information, i.e. because certain information are available only to few market participants. In financial markets, jump effects fade away as time passes: On the one hand, if the stock price falls, new investors are motivated to buy the stock. On the other hand, a rise of the stock price may lead to profit-taking, i.e. some investors sell the stock in order to lock in gains. Shot noise models are based on Merton's jump diffusion models where the decline of the jump effect after a price jump is neglected. In contrast to jump diffusion models, shot noise models respect the decay of jump effects. In complete markets, the so-called equivalent martingale measure is used to price European options and for hedging. Since stock price models incorporating jumps describe incomplete markets, the equivalent martingale measure cannot be determined uniquely. Hence, in this thesis, we deduce the so-called equivalent minimal martingale measure, both in discrete and continuous time. In contrast to Merton's jump diffusion models and to the well-known pricing model of Black and Scholes, the presented shot noise models are able to reproduce volatility smile effects which can be observed in financial markets.
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 Discontinuous Interest Rate Processes written by Mukarram Attari and published by . This book was released on 2012 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper obtains equilibrium interest rate option prices for discontinuous short-term interest rate processes. The prices are first obtained for a general distribution of jump sizes using a process with a number of fixed sized jumps. The option price is the expectation, over the number and timing of jumps, of the option price given the number and timing of the jumps. This is similar in form to Merton's jump-diffusion option pricing formula for stock options. The differences are that (i) this paper does not need the assumption that jump risk is not priced and (ii) the timing of the jumps is also important. The pricing formulas are then used to obtain option prices when the jump distribution is known to be one of the continuous distributions. The commonly used jump-diffusion and stochastic volatility diffusion option prices can be obtained as limiting cases. The paper shows how portfolios to hedge derivative securities can be built.
Download or read book American Options in L vy Models with Stochastic Interest Rates written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. An explicit algorithm for the case of positive stochastic interest rates driven by a process of the Ornstein-Uhlenbeck type is derived. Efficiency of the method is illustrated with numerical examples.
Download or read book American Options in Levy Models With Stochastic Interest Rate of CIR Type written by Svetlana Boyarchenko and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of interest rate driven by the square root process with embedded jumps is derived. Numerical examples show that fairly accurate results can be obtained in reasonable time. It is shown that the shape of the early exercise boundary strongly depends on the sign of the leverage parameter.
Download or read book Option Prices in Stochastic Volatility Models written by Giulia Terenzi and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study option pricing problems in stochastic volatility models. In the first part of this thesis we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic obstacle problem. Our approach is based on variational inequalities in suitable weighted Sobolev spaces and extends recent results of Daskalopoulos and Feehan (2011, 2016) and Feehan and Pop (2015). We also investigate the properties of the American value function. In particular, we prove that, under suitable assumptions on the payoff, the value function is nondecreasing with respect to the volatility variable. Then, we focus on an American put option and we extend some results which are well known in the Black and Scholes world. In particular, we prove the strict convexity of the value function in the continuation region, some properties of the free boundary function, the Early Exercise Price formula and a weak form of the smooth fit principle. This is done mostly by using probabilistic techniques.In the second part we deal with the numerical computation of European and American option prices in jump-diffusion stochastic volatility models. We first focus on the Bates-Hull-White model, i.e. the Bates model with a stochastic interest rate. We consider a backward hybrid algorithm which uses a Markov chain approximation (in particular, a “multiple jumps” tree) in the direction of the volatility and the interest rate and a (deterministic) finite-difference approach in order to handle the underlying asset price process. Moreover, we provide a simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods.Finally, we analyze the rate of convergence of the hybrid algorithm applied to general jump-diffusion models. We study first order weak convergence of Markov chains to diffusions under quite general assumptions. Then, we prove the convergence of the algorithm, by studying the stability and the consistency of the hybrid scheme, in a sense that allows us to exploit the probabilistic features of the Markov chain approximation.
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 American Options in Regime Switching L vy Models With Non Semibounded Stochastic Interest Rates written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. Contrary to the earlier version of the method, the interest rate may assume non-positive values. As applications, explicit algorithms for Vasicek and Black's models with jumps are derived. Numerical examples show that the option prices in these two models are very close.
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 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 Equilibrium Option Valuation with Systematic Stochastic Volatility written by Kaushik I. Amin and published by . This book was released on 1992 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Option Valuation with Systematic Stochastic Volatility written by Kaushik I. Amin and published by . This book was released on 1992 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Financial Option Valuation written by Desmond J. Higham and published by Cambridge University Press. This book was released on 2004-04-15 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.
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
