Analytical Derivatives for Markov Switching Models PDF Download
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Author: Jeff Gable
Publisher:
ISBN: 9780662236856
Category : Markov processes
Languages : en
Pages : 24
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Book Description
Author: Jeff Gable
Publisher:
ISBN: 9780662236856
Category : Markov processes
Languages : en
Pages : 24
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Book Description
Author: Kun Fan
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 198
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Book Description
Author: Yi Tang
Publisher: World Scientific
ISBN: 9812706658
Category : Business & Economics
Languages : en
Pages : 523
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Book Description
This book addresses selected practical applications and recent developments in the areas of quantitative financial modeling in derivatives instruments, some of which are from the authorsOCO own research and practice. While the primary scope of this book is the fixed-income market (with further focus on the interest rate market), many of the methodologies presented also apply to other financial markets, such as the credit, equity, and foreign exchange markets. This book, which assumes that the reader is familiar with the basics of stochastic calculus and derivatives modeling, is written from the point of view of financial engineers or practitioners, and, as such, it puts more emphasis on the practical applications of financial mathematics in the real market than the mathematics itself with precise (and tedious) technical conditions. It attempts to combine economic insights with mathematics and modeling so as to help the reader develop intuitions. In addition, the book addresses the counterparty credit risk modeling, pricing, and arbitraging strategies, which are relatively recent developments and are of increasing importance. It also discusses various trading structuring strategies and touches upon some popular credit/IR/FX hybrid products, such as PRDC, TARN, Snowballs, Snowbears, CCDS, credit extinguishers."
Author: Maddalena Cavicchioli
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In this work, we give simple matrix formulae for maximum likelihood estimates of parameters in a broad class of vector autoregressions subject to Markovian changes in regime. This allows us to determine explicitly the asymptotic variance-covariance matrix of the estimators, giving a concrete possibility for the use of the classical testing procedures. In the context of multivariate autoregressive conditional heteroskedastic models with changes in regime, we provide formulae for the analytic derivatives of the log likelihood. Then we prove the consistency of some maximum likelihood estimators and give some formulae for the asymptotic variance of the different estimators.
Author: Farzad Alavi Fard
Publisher:
ISBN:
Category : Derivative securities
Languages : en
Pages : 113
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Book Description
In this thesis we argue that regime-switching models can significantly improve the pricing models for financial derivatives. We use three examples to analyse the valuation of derivative contracts under the Markovian regime-switching framework, namely, 1) a European call option, 2) a Ruin Contingent Life Annuity, and 3) a participating product. Such a regime-switching framework unveils a potent class of models. Throughout the modulation of the model parameters by a Markov chain, they can simultaneously explain the asymmetic leptokurtic features of the returns' distribution, as well as the volatility smile and the volatility clustering effect. The intuition behind regime-switching models is to capture the appealing idea that the macro-economy is subjected to regular, yet unpredictable in time, states, which in turn affects the prices of financial securities.
Author: George Yin
Publisher: Springer
ISBN: 3030254984
Category : Mathematics
Languages : en
Pages : 599
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Book Description
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
Author: Hal Caswell
Publisher: Springer
ISBN: 3030105342
Category : Social Science
Languages : en
Pages : 308
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Book Description
This open access book shows how to use sensitivity analysis in demography. It presents new methods for individuals, cohorts, and populations, with applications to humans, other animals, and plants. The analyses are based on matrix formulations of age-classified, stage-classified, and multistate population models. Methods are presented for linear and nonlinear, deterministic and stochastic, and time-invariant and time-varying cases. Readers will discover results on the sensitivity of statistics of longevity, life disparity, occupancy times, the net reproductive rate, and statistics of Markov chain models in demography. They will also see applications of sensitivity analysis to population growth rates, stable population structures, reproductive value, equilibria under immigration and nonlinearity, and population cycles. Individual stochasticity is a theme throughout, with a focus that goes beyond expected values to include variances in demographic outcomes. The calculations are easily and accurately implemented in matrix-oriented programming languages such as Matlab or R. Sensitivity analysis will help readers create models to predict the effect of future changes, to evaluate policy effects, and to identify possible evolutionary responses to the environment. Complete with many examples of the application, the book will be of interest to researchers and graduate students in human demography and population biology. The material will also appeal to those in mathematical biology and applied mathematics.
Author: Gongqiu Zhang
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Diffusion models with non-smooth coefficients often appear in financial applications, with examples including but not limited to threshold models for financial variables, the pricing of occupation time derivatives and shadow rate models for interest rate dynamics. To calculate the expected value of a discounted payoff under general state-dependent discounting and monitoring of barrier crossing, continuous time Markov chain (CTMC) approximation can be applied. In a recent work, Zhang and Li (2018, Operations Research, forthcoming) established sharp convergence rates of CTMC approximation for diffusion models with smooth coefficients but non-smooth payoff functions, and proposed grid design principles to ensure nice convergence behaviors. However, their theoretical analysis fails to obtain sharp convergence rates when model coefficients lack smoothness. Moreover, it is unclear how to design the grid of CTMC to remedy the inferior convergence behaviors resulting from non-smooth model coefficients. In this paper, we introduce new ways for the theoretical analysis of CTMC approximation for general diffusion models with non-smooth coefficients. We prove that convergence of option price is only first order in general. However, strikingly, if all the discontinuous points of the model coefficients and the payoff function are in the midway between two grid points, second order convergence in the maximum norm is restored and in this case, delta and gamma have second order convergence at almost all grid points except those next to the discontinuous points. Numerical experiments are conducted that confirm the validity of our theoretical results. We also compare the CTMC approximation approach with properly designed grids to a classical numerical PDE scheme for diffusion models with non-smooth coefficients, where the finite difference method is applied separately in each region with smooth coefficients and continuous pasting of the value function is enforced at the discontinuities. We show that our approach is superior to the latter in terms of both the convergence rate and the simplicity of implementation.
Author: Simon van Norden
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
This paper is a user's guide to a set of Gauss procedures developed at the Bank of Canada for estimating regime-switching models. The procedures can estimate relatively quickly a wide variety of switching models and so should prove useful to the applied researcher. Sample program listings are included. FRENCH VERSION La presente etude constitue un guide d'utilisation d'un ensemble de procedures de Gauss mises au point a la Banque du Canada en vue de l'estimation des modeles a changement de regime. Ces procedures permettent d'estimer de facon assez rapide une vaste gamme de modeles a changement de regime et devraient s'averer utiles pour la recherche appliquee. Des echantillons de programmes sont inclus dans l'etude.
Author:
Publisher:
ISBN:
Category : Canada
Languages : en
Pages : 36
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Book Description
