Download or read book Option Pricing for an Affine Jump Diffusion Model written by Zhiqiu Li and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first part of this thesis, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion (AJD) model. Let log stock price under risk-neutral measure follow an AJD model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the G\"{a}rtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are also studied. Numerical results are provided to validate the theoretical work. In the second part of this thesis, we study the European option pricing problem when the underlying stock follows an AJD model whose jump interarrival time has a Cox-Ingersoll-Ross type intensity dynamics. An analytic formula of a European option pricing is derived using the Fourier inversion transform technique. We develop a Monte Carlo algorithm to simulate the dynamics of an AJD model. We observe AJD At-The-Money (ATM) European option prices using the Monte Carlo simulation converge to the Fourier analytic ones as the number of simulation paths increases.

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 Transform Analysis and Asset Pricing for Affine Jump diffusions written by Darrell Duffie and published by . This book was released on 1999 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the setting of affine' jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensityy-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option 'smirks' of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both amplitude as well as jump timing.

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 Affine POD Galerkin Schemes for Option Pricing in Jump diffusion Models written by Jianjie Lu and published by . This book was released on 2014 with total page 158 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 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 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 American Option Pricing in a Jump Diffusion Model written by Jeremy Berros and published by LAP Lambert Academic Publishing. This book was released on 2010-09 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many alternative models have been developed lately to generalize the Black-Scholes option pricing model in order to incorporate more empirical features. Brownian motion and normal distribution have been used in this Black-Scholes option-pricing framework to model the return of assets. However, two main points emerge from empirical investigations: (i) the leptokurtic feature that describes the return distribution of assets as having a higher peak and two asymmetric heavier tails than those of the normal distribution, and (ii) an empirical phenomenon called "volatility smile" in option markets. Among the recent models that addressed the aforementioned issues is that of Kou (2002), which allows the price of the underlying asset to move according to both Brownian increments and double-exponential jumps. The aim of this thesis is to develop an analytic pricing expression for American options in this model that enables us to e±ciently determine both the price and related hedging parameters.

Download or read book Option Pricing in the Jump diffusion Model with a Random Junp Amplitude written by B. Jensen and published by . This book was released on 1999 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Transform Analysis of Affine Jump Diffusion Processes with Applications to Asset Pricing written by Claude Rodrigue Bambe Moutsinga and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a class of models in asset pricing, whose underlying has dynamics of Affine jump diffusion type. We first present L evy processes with their properties. We then introduce Affine jump diffusion processes which are basically a particular class of L evy processes. Our motivation for these is driven by the fact that many financial models are built on them. Affine jump diffusion processes present good analytical properties that allow one to get close form formulas for a wide range of option pricing. The approach we use here is based on the paper by Duffie D, Pan J, and Singleton K. An example will show how incorporating parameters such as the volatility of the underlying asset in the model, can influence the resulting price of the financial instrument under consideration. We will also show how this class of models incorporate well known models, specially those used to model interest rates dynamics, like for instance the Vasicek model.

Download or read book Option Pricing Utilizing a Jump Diffusion Model with a Log Mixture Normal Jump Distribution written by Thomas Lonon and published by . This book was released on 2013 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Modeling And Computation In Finance With Exercises And Python And Matlab Computer Codes written by Cornelis W Oosterlee and published by World Scientific. This book was released on 2019-10-29 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.Supplementary Material:Solutions Manual is available to instructors who adopt this textbook for their courses. Please contact [email protected].

Download or read book Option Pricing and Jump diffusion Models written by Zongwu Zhu and published by . This book was released on 2005 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Jump Diffusion Model for Option Pricing written by Steven Kou and published by . This book was released on 2001 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract_Content: Brownian motion and normal distribution have been widely used in the Black-Scholes option pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical abnormity called quot;volatility smile'' in option pricing. To incorporate both of them, this paper proposes, for the purpose of option pricing, a double exponential jump diffusion model. The main attraction of the model is its simplicity. In particular, it is simple enough to derive analytical solutions for a variety of option pricing problems, including call and put options, interest rate derivatives and path-dependent options; it seems impossible for many other alternative models to do this. Equilibrium analysis and a psychological interpretation of the model are also presented.

Download or read book Consistency Conditions for Affine Term Structure Models Ii Option Pricing Under Diffusions with Embedded Jumps written by Sergei Levendorskii and published by . This book was released on 2005 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sufficient conditions for the application of the Feynman-Kac formula for option pricing for wide classes of affine term structure models in the jump-diffusion case are derived generalizing earlier results for bond pricing in the pure diffusion case.