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Author: Zhenhao Zhou Publisher: ISBN: Category : Mathematical models Languages : en Pages : 110
Book Description
Motivated by the Guaranteed Minimum Death Benefits (GMDB) in variable annuities, we are interested in valuing equity-linked options whose expiry date is the time of the death of the policyholder. Because the time-until-death distribution can be approximated by linear combinations of exponential distributions or mixtures of Erlang distributions, the analysis can be reduced to the case where the time-until-death distribution is exponential or Erlang. We present two probability methods to price American options with an exponential expiry date. Both methods give the same results. An American option with Erlang expiry date can be seen as an extension of the exponential expiry date case. We calculate its price as the sum of the price of the corresponding European option and the early exercise premium. Because the optimal exercise boundary takes the form of a staircase, the pricing formula is a triple sum. We determine the optimal exercise boundary recursively by imposing the "smooth pasting" condition. The examples of the put option, the exchange option, and the maximum option are provided to illustrate how the methods work. Another issue related to variable annuities is the surrender behavior of the policyholders. To model this behavior, we suggest using barrier options. We generalize the reflection principle and use it to derive explicit formulas for outside barrier options, double barrier options with constant barriers, and double barrier options with time varying exponential barriers. Finally, we provide a method to approximate the distribution of the time-until-death random variable by combinations of exponential distributions or mixtures of Erlang distributions. Compared to directly fitting the distributions, my method has two advantages: 1) It is more robust to the initial guess. 2) It is more likely to obtain the global minimizer.
Author: Zhenhao Zhou Publisher: ISBN: Category : Mathematical models Languages : en Pages : 110
Book Description
Motivated by the Guaranteed Minimum Death Benefits (GMDB) in variable annuities, we are interested in valuing equity-linked options whose expiry date is the time of the death of the policyholder. Because the time-until-death distribution can be approximated by linear combinations of exponential distributions or mixtures of Erlang distributions, the analysis can be reduced to the case where the time-until-death distribution is exponential or Erlang. We present two probability methods to price American options with an exponential expiry date. Both methods give the same results. An American option with Erlang expiry date can be seen as an extension of the exponential expiry date case. We calculate its price as the sum of the price of the corresponding European option and the early exercise premium. Because the optimal exercise boundary takes the form of a staircase, the pricing formula is a triple sum. We determine the optimal exercise boundary recursively by imposing the "smooth pasting" condition. The examples of the put option, the exchange option, and the maximum option are provided to illustrate how the methods work. Another issue related to variable annuities is the surrender behavior of the policyholders. To model this behavior, we suggest using barrier options. We generalize the reflection principle and use it to derive explicit formulas for outside barrier options, double barrier options with constant barriers, and double barrier options with time varying exponential barriers. Finally, we provide a method to approximate the distribution of the time-until-death random variable by combinations of exponential distributions or mixtures of Erlang distributions. Compared to directly fitting the distributions, my method has two advantages: 1) It is more robust to the initial guess. 2) It is more likely to obtain the global minimizer.
Author: Anna Rita Bacinello Publisher: ISBN: Category : Languages : en Pages : 16
Book Description
In this paper we describe an algorithm based on the Least Squares Monte Carlo method to price life insurance contracts embedding American options. We focus on equity-linked contracts with surrender options and terminal guarantees on benefits payable upon death, survival and surrender. The framework allows for randomness in mortality as well as stochastic volatility and jumps in financial risk factors. We provide numerical experiments demonstrating the performance of the algorithm in the context of multiple risk factors and exercise dates.
Author: Marco Corazza Publisher: Springer ISBN: 331902499X Category : Mathematics Languages : en Pages : 312
Book Description
The interaction between mathematicians and statisticians has been shown to be an effective approach for dealing with actuarial, insurance and financial problems, both from an academic perspective and from an operative one. The collection of original papers presented in this volume pursues precisely this purpose. It covers a wide variety of subjects in actuarial, insurance and finance fields, all treated in the light of the successful cooperation between the above two quantitative approaches. The papers published in this volume present theoretical and methodological contributions and their applications to real contexts. With respect to the theoretical and methodological contributions, some of the considered areas of investigation are: actuarial models; alternative testing approaches; behavioral finance; clustering techniques; coherent and non-coherent risk measures; credit scoring approaches; data envelopment analysis; dynamic stochastic programming; financial contagion models; financial ratios; intelligent financial trading systems; mixture normality approaches; Monte Carlo-based methods; multicriteria methods; nonlinear parameter estimation techniques; nonlinear threshold models; particle swarm optimization; performance measures; portfolio optimization; pricing methods for structured and non-structured derivatives; risk management; skewed distribution analysis; solvency analysis; stochastic actuarial valuation methods; variable selection models; time series analysis tools. As regards the applications, they are related to real problems associated, among the others, to: banks; collateralized fund obligations; credit portfolios; defined benefit pension plans; double-indexed pension annuities; efficient-market hypothesis; exchange markets; financial time series; firms; hedge funds; non-life insurance companies; returns distributions; socially responsible mutual funds; unit-linked contracts. This book is aimed at academics, Ph.D. students, practitioners, professionals and researchers. But it will also be of interest to readers with some quantitative background knowledge.
Author: Mary Hardy Publisher: John Wiley & Sons ISBN: 0471392901 Category : Business & Economics Languages : en Pages : 309
Book Description
A comprehensive guide to investment guarantees in equity-linked life insurance Due to the convergence of financial and insurance markets, new forms of investment guarantees are emerging which require financial service professionals to become savvier in modeling and risk management. With chapters that discuss stock return models, dynamic hedging, risk measures, Markov Chain Monte Carlo estimation, and much more, this one-stop reference contains the valuable insights and proven techniques that will allow readers to better understand the theory and practice of investment guarantees and equity-linked insurance policies. Mary Hardy, PhD (Waterloo, Ontario, Canada), is an Associate Professor and Associate Chair of Actuarial Science at the University of Waterloo and is a Fellow of the Institute of Actuaries and an Associate of the Society of Actuaries, where she is a frequent speaker. Her research covers topics in life insurance solvency and risk management, with particular emphasis on equity-linked insurance. Hardy is an Associate Editor of the North American Actuarial Journal and the ASTIN Bulletin and is a Deputy Editor of the British Actuarial Journal.
Author: Aswath Damodaran Publisher: John Wiley & Sons ISBN: 1118808932 Category : Business & Economics Languages : en Pages : 663
Book Description
Aswath Damodaran, distinguished author, Professor of Finance, and David Margolis, Teaching Fellow at the NYU Stern School of Business, has delivered the newest edition of Applied Corporate Finance. This readable text provides the practical advice students and practitioners need rather than a sole concentration on debate theory, assumptions, or models. Like no other text of its kind, Applied Corporate Finance, 4th Edition applies corporate finance to real companies. It now contains six real-world core companies to study and follow. Business decisions are classified for students into three groups: investment, financing, and dividend decisions.
Author: Svetlana I. Boyarchenko Publisher: World Scientific ISBN: 9810249446 Category : Business & Economics Languages : en Pages : 421
Book Description
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lvy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory.The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential operators technique in non-Gaussian situations. The authors also consider discrete time analogues of perpetual American options and the problem of the optimal choice of capital, and outline several possible directions in which the methods of the book can be developed further.Taking account of a diverse audience, the book has been written in such a way that it is simple at the beginning and more technical in further chapters, so that it is accessible to graduate students in relevant areas and mathematicians without prior knowledge of finance or economics.
Author: Timothy Irwin Publisher: World Bank Publications ISBN: 0821368591 Category : Business & Economics Languages : en Pages : 230
Book Description
The book considers when governments should give guarantees to private investors. After describing the history of guarantees, and the challenges the politics and psychology create for good decisions, the book sets out a principles for allocating risk (and therefore guarantees), techniques for valuing guarantees, and rules to encourage good decisions.
Author: Great Britain. Treasury Publisher: Stationery Office ISBN: 9780115601071 Category : Business & Economics Languages : en Pages : 114
Book Description
This new edition incorporates revised guidance from H.M Treasury which is designed to promote efficient policy development and resource allocation across government through the use of a thorough, long-term and analytically robust approach to the appraisal and evaluation of public service projects before significant funds are committed. It is the first edition to have been aided by a consultation process in order to ensure the guidance is clearer and more closely tailored to suit the needs of users.
Author: Collectif Publisher: OECD ISBN: 9264267794 Category : Business & Economics Languages : en Pages : 108
Book Description
This publication helps policy makers to better understand annuity products and the guarantees they provide in order to optimise the role that these products can play in financing retirement. Product design is a crucial factor in the potential role of annuity products within the pension system, along with the cost and demand for these products, and the resulting risks that are borne by the annuity providers. Increasingly complex products, however, pose additional challenges concerning consumer protection. Consumers need to be aware of their options and have access to unbiased and comprehensible advice and information about these products.
Author: Frank J. Fabozzi Publisher: CFA Institute Research Foundation ISBN: 1944960341 Category : Business & Economics Languages : en Pages : 234
Book Description
The price at which a stock is traded in the market reflects the ability of the firm to generate cash flow and the risks associated with generating the expected future cash flows. The authors point to the limits of widely used valuation techniques. The most important of these limits is the inability to forecast cash flows and to determine the appropriate discount rate. Another important limit is the inability to determine absolute value. Widely used valuation techniques such as market multiples - the price-to-earnings ratio, firm value multiples or a use of multiple ratios, for example - capture only relative value, that is, the value of a firm's stocks related to the value of comparable firms (assuming that comparable firms can be identified). The study underlines additional problems when it comes to valuing IPOs and private equity: Both are sensitive to the timing of the offer, suffer from information asymmetry, and are more subject to behavioral elements than is the case for shares of listed firms. In the case of IPOs in particular, the authors discuss how communication strategies and media hype play an important role in the IPO valuation/pricing process.
Author: Zhenhao Zhou
Author: Zhenhao Zhou
Author: Anna Rita Bacinello
Author: Marco Corazza
Author: Mary Hardy
Author: Aswath Damodaran
Author: Svetlana I. Boyarchenko
Author: Timothy Irwin
Author: Great Britain. Treasury
Author: Collectif
Author: Frank J. Fabozzi