Author: Holger Maria FinkPublisher:
ISBN:
Category :
Languages : en
Pages : 176
Book Description
Stochastic Processes Beyond Semimartingales with Application to Interest Rates, Credit Risk and Volatility Modeling
Author: Holger Maria FinkPolynomial Semimartingales and a Deep Learning Approach to Local Stochastic Volatility Calibration
Author: Wahid Khosrawi-SardroudiPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Abstract: Financial markets have experienced a precipitous increase in complexity over the past decades, posing a significant challenge from a risk management point of view. This complexity motivates the application and development of sophisticated models based on the theory of stochastic processes and in particular stochastic calculus. In this regard, the contribution of this thesis is twofold, namely by extending the class if tractable stochastic processes in form of polynomial processes and polynomial semimartingales and by showing how efficient calibration of local stochastic volatility models is possible by applying machine learning techniques. In the first part - the main part - we extend the class of polynomial processes that has previously been established to include beyond stochastic discontinuity. This extension is motivated by the fact that certain events in financial markets take place at a deterministic time point but without foreseeable outcome. Such events consist e.g. of decisions regarding interest rates of central banks or political elections/votes. Since the outcome has a significant impact on markets, it is therefore desirable to consider stochastic processes, that can reproduce such jumps at previously specified time points. Such an extension has already been introduced in the affine framework. We will show that similar modifications hold true in the polynomial case. In particular, we will show how after this extension, computation of mixed moments in a multivariate setting reduces to solving a measure ordinary differential equation, posing a significant reduction in complexity to the measure partial differential case in the context of Kolmogorow equations. A central role in the theory of time-homogeneous polynomial processes is played by the theory of one parameter matrix semigroups. Hence, we will develop a two parameter version of the matrix semigroup theory under lower regularity then what exists in the literature. This accounts for time-inhomogeneity of the stochastic processes we consider. While in the one parameter case, full regularity follows already from very mild assumptions, we will see that this is not the case anymore in the two parameter case. In the second part of this thesis we investigate a more applied topic, namely the exact calibration of local stochastic volatility models to financial data. We show how this computationally challenging problem can be efficiently solved by applying machine learning te ...
Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
Author: Jean-Pierre FouquePublisher: Cambridge University Press
ISBN: 113950245X
Category : Mathematics
Languages : en
Pages : 456
Book Description
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
Stochastic Processes And Applications To Mathematical Finance - Proceedings Of The Ritsumeikan International Symposium
Author: Jiro AkahoriPublisher: World Scientific
ISBN: 9814483095
Category : Mathematics
Languages : en
Pages : 410
Book Description
This book contains 17 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Lévy processes, stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings® (ISSHP® / ISI Proceedings)• Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Two Essays on Multivariate Stochastic Processes and Applications to Credit Risk Modeling
Author: Luca VidozziIntroduces Stochastic Processes in Mathematical Finance
Author: Oleg KritskiPublisher: LAP Lambert Academic Publishing
ISBN: 9783848407194
Category :
Languages : en
Pages : 172
Book Description
This monograph gives an overview of current methods for solving to stochastic differencial equations both analytical and numerical and considers several applications of mathematical finance models in the context of derivative pricing. In particular, credit risk models are incorporated into the pricing of derivative contracts such as CDS with counterparty default risk etc. Also, monograph introduces contingent claims theory and summarizes some important applications such as Black-Sholes formulae computed for options on shares and futures, Chapmen-Kolmogorov equation, Heath-Jarrow-Morton methodology for interest-rate modeling.
Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
Author: Jean-Pierre FouquePublisher: Cambridge University Press
ISBN: 9780521843584
Category : Mathematics
Languages : en
Pages : 456
Book Description
Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM "beta," and the Heston model and generalizations of it. "Off-the-shelf" formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.
Modeling Stochastic Volatility with Application to Stock Returns
Author: Mr.Noureddine KrichenePublisher: International Monetary Fund
ISBN: 1451854846
Category : Business & Economics
Languages : en
Pages : 30
Book Description
A stochastic volatility model where volatility was driven solely by a latent variable called news was estimated for three stock indices. A Markov chain Monte Carlo algorithm was used for estimating Bayesian parameters and filtering volatilities. Volatility persistence being close to one was consistent with both volatility clustering and mean reversion. Filtering showed highly volatile markets, reflecting frequent pertinent news. Diagnostics showed no model failure, although specification improvements were always possible. The model corroborated stylized findings in volatility modeling and has potential value for market participants in asset pricing and risk management, as well as for policymakers in the design of macroeconomic policies conducive to less volatile financial markets.
Stochastic Processes and Applications to Mathematical Finance
Author: Jiro AkahoriPublisher: World Scientific Publishing Company Incorporated
ISBN: 9812565191
Category : Business & Economics
Languages : en
Pages : 217
Book Description
Based around recent lectures given at the prestigious Ritsumeikan conference, the tutorial and expository articles contained in this volume are an essential guide for practitioners and graduates alike who use stochastic calculus in finance. Among the eminent contributors are Paul Malliavin and Shinzo Watanabe, pioneers of Malliavin Calculus. The coverage also includes a valuable review of current research on credit risks in a mathematically sophisticated way contrasting with existing economics-oriented articles.
Author: Roberto Casarin