Download or read book Pricing and Hedging Under High dimensional Jump diffusion Models Using Partial Differential Equations written by Peter Thomas Hepperger and published by . This book was released on 2011 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Simplified Method for Hedging Jump Diffusions written by Wenjie Xiao and published by . This book was released on 2010 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Brownian Motion (GBM) and has been widely used in the Black Scholes option-pricing framework to model the return of assets. However, many empirical investigations show that market returns have higher peaks and fatter tails than GBM. Contrary to the Black Scholes model, an option-pricing model which contains jumps reflects the evolution of stock prices more accurately. Therefore, hedging a model under jump diffusion would be desirable. This thesis develops a simplified method for hedging jump diffusions. In order to hedge the jump risk, other instruments besides the underlying asset must be used in the hedging procedure. We start with a the Partial Integro Differential Equation (PIDE) that models contingent claims with jumps and consider a dynamic hedging strategy that uses a hedging portfolio with the underlying asset and liquidly traded options. We introduce a simple hedging method, where, at each rebalance time, we minimize the instantaneous jump risk by finding proper weights for the underlying asset and instruments. We use a simulation method to test our approach using a Truncated SVD method to solve the linear system of equations resulting from our minimization procedure. Our results indicate that the proposed dynamic hedging strategy provides sufficient protection against diffusion and jump risk. The method also provides a firm theoretical basis for a method which is used in practice.
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 Random Motions in Markov and Semi Markov Random Environments 2 written by Anatoliy Pogorui and published by John Wiley & Sons. This book was released on 2021-01-11 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.
Download or read book The Time Discrete Method of Lines for Options and Bonds written by Gunter H. Meyer and published by World Scientific Publishing Company Incorporated. This book was released on 2014-11-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusion equations in finance. In The Time-Discrete Method of Lines for Options and Bonds, Gunter H Meyer examines PDE models for financial derivatives and shows where the Fichera theory requires the pricing equation at degenerate boundary points, and what modifications of it lead to acceptable tangential boundary conditions at non-degenerate points on computational boundaries when no financial data are available. Extensive numerical simulations are carried out with the method of lines to examine the influence of the finite computational domain and of the chosen boundary conditions on option and bond prices in one and two dimensions, reflecting multiple assets, stochastic volatility, jump diffusion and uncertain parameters. Special emphasis is given to early exercise boundaries, prices and their derivatives near expiration. Detailed graphs and tables are included which may serve as benchmark data for solutions found with competing numerical methods.
Download or read book The Pricing and the Hedging of Equity Derivatives with Affine Jump Diffusion Models written by Paolo Verzella and published by . This book was released on 2006 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pricing Derivatives Under L vy Models written by Andrey Itkin and published by . This book was released on 2017 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient Numerical Approximation of Solutions to High dimensional Partial Differential Equations written by Jacob Snoeijer and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pricing and Hedging for Incomplete Jump Diffusion Benchmark Models written by Eckhard Platen and published by . This book was released on 2003 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete time Bond and Option Pricing for Jump diffusion Processes written by Sanjiv R. Das and published by . This book was released on 1994 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a methodology for pricing American type interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite-differencing approach to deal with partial differential-difference equations derived in a jump-diffusion world. The numerical stability and convergence of the scheme is also proved. Numerical illustrations compare jump-diffusion and pure-diffusion models. Whereas the existence of jumps affects call options on bonds very much like those on stocks, this is not the case for puts which are affected by the asymmetric convexity of the bond pricing function. Early exercise behavior is also analyzed.
Download or read book Numerical Solution of Stochastic Differential Equations written by Peter E. Kloeden and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Download or read book Discrete time Bond and Option Pricing for Jump diffusion Processes written by Sanjiv R. Das and published by . This book was released on 1994 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a methodology for pricing American type interest rate contingent claims for jump-diffusion processes. The method enhances the standard finite-differencing approach to deal with partial differential-difference equations derived in a jump-diffusion world. The numerical stability and convergence of the scheme is also proved. Numerical illustrations compare jump-diffusion and pure-diffusion models. Whereas the existence of jumps affects call options on bonds very much like those on stocks, this is not the case for puts which are affected by the asymmetric convexity of the bond pricing function. Early exercise behavior is also analyzed.
Download or read book Handbooks in Operations Research and Management Science Financial Engineering written by John R. Birge and published by Elsevier. This book was released on 2007-11-16 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: The remarkable growth of financial markets over the past decades has been accompanied by an equally remarkable explosion in financial engineering, the interdisciplinary field focusing on applications of mathematical and statistical modeling and computational technology to problems in the financial services industry. The goals of financial engineering research are to develop empirically realistic stochastic models describing dynamics of financial risk variables, such as asset prices, foreign exchange rates, and interest rates, and to develop analytical, computational and statistical methods and tools to implement the models and employ them to design and evaluate financial products and processes to manage risk and to meet financial goals. This handbook describes the latest developments in this rapidly evolving field in the areas of modeling and pricing financial derivatives, building models of interest rates and credit risk, pricing and hedging in incomplete markets, risk management, and portfolio optimization. Leading researchers in each of these areas provide their perspective on the state of the art in terms of analysis, computation, and practical relevance. The authors describe essential results to date, fundamental methods and tools, as well as new views of the existing literature, opportunities, and challenges for future research.
Download or read book Backward Stochastic Differential Equations written by N El Karoui and published by CRC Press. This book was released on 1997-01-17 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the texts of seminars presented during the years 1995 and 1996 at the Université Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on the hypotheses are introduced to obtain more general results.
Download or read book Partial Differential Equations in Action written by Sandro Salsa and published by Springer. This book was released on 2015-04-24 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.
Download or read book Basket Options Pricing for Jump Diffusion Models written by 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 INFORMS Annual Meeting written by Institute for Operations Research and the Management Sciences. National Meeting and published by . This book was released on 2008 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
