Risk Measures and Optimal Strategies for Discrete Hedging PDF Download

Author: Maria-Cristina Patron
Publisher:
ISBN:
Category :
Languages : en
Pages : 346

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Author: Artur Sepp
Publisher:
ISBN:
Category :
Languages : en
Pages : 37

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Book Description
We consider the delta-hedging strategy for a vanilla option under the discrete hedging and transaction costs, assuming that an option is delta-hedged using the Black-Scholes-Merton model with the log-normal volatility implied by the market price of the option. We analyze the expected profit-and-loss (P&L) of the delta-hedging strategy assuming the four possible dynamics of asset returns under the statistical measure: the log-normal diffusion, the jump-diffusion, the stochastic volatility and the stochastic volatility with jumps. For all of the four models, we derive analytic formulas for the expected P&L, expected transaction costs, and P&L volatility assuming hedging at fixed times. Using these formulas, we formulate the problem of finding the optimal hedging frequency to maximize the Sharpe ratio of the delta-hedging strategy. Also, we show that the Sharpe ratio of the delta-hedging strategy can be improved by incorporating the price and delta bands for the rebalancing of the delta-hedge and provide analytical approximations for computing the optimal bands in our optimization approach. As illustrations, we show that our method provides a very good approximation to the actual Sharpe ratio obtained by Monte Carlo simulations under the time-based re-hedging. In contrary to Monte Carlo simulations, our analytic approach provide a fast and an accurate way to estimate the risk-reward characteristic of the delta-hedging strategy for real time computations.

Author: Hans Föllmer
Publisher: Walter de Gruyter
ISBN: 3110218054
Category : Mathematics
Languages : en
Pages : 557

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Book Description
This book is an introduction to financial mathematics. It is intended for graduate students in mathematics and for researchers working in academia and industry. The focus on stochastic models in discrete time has two immediate benefits. First, the probabilistic machinery is simpler, and one can discuss right away some of the key problems in the theory of pricing and hedging of financial derivatives. Second, the paradigm of a complete financial market, where all derivatives admit a perfect hedge, becomes the exception rather than the rule. Thus, the need to confront the intrinsic risks arising from market incomleteness appears at a very early stage. The first part of the book contains a study of a simple one-period model, which also serves as a building block for later developments. Topics include the characterization of arbitrage-free markets, preferences on asset profiles, an introduction to equilibrium analysis, and monetary measures of financial risk. In the second part, the idea of dynamic hedging of contingent claims is developed in a multiperiod framework. Topics include martingale measures, pricing formulas for derivatives, American options, superhedging, and hedging strategies with minimal shortfall risk. This third revised and extended edition now contains more than one hundred exercises. It also includes new material on risk measures and the related issue of model uncertainty, in particular a new chapter on dynamic risk measures and new sections on robust utility maximization and on efficient hedging with convex risk measures.

Author: Nicholas H. Bingham
Publisher: Springer Science & Business Media
ISBN: 1447138562
Category : Mathematics
Languages : en
Pages : 447

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Book Description
This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.

Author: Gang Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
The use of futures contracts as hedging instruments to reduce risk has been the focus of much research. Various risk measures have been developed and have subsequently been employed in an effort to create hedging strategies and to calculate optimal hedge ratios. This thesis proposes a more generalized risk model to measure the risk of hedged assets. The five-parameter model presented herein assumes that each investor has a different target return, level of risk aversion, and degree of sensitivity to lower and higher partial moments. The optimal hedging activity for each investor should then seek to minimize the unique generalized risk measure. This paper utilizes an out-of-sample test on a hedged position in the S & P500 index in the period from December 1982 to December 2004. Tests are conducted to determine whether the change of target returns and sensitivity parameters will affect optimal hedge ratios. In addition, whether hedging effectiveness changes significantly in-sample versus out-of-sample, and between each model and a naïve hedging strategy is investigated. Also, mean returns of hedged portfolios are compared for various models. This thesis makes three important contributions. First, this study is the first to implement both higher and lower partial moments in the determination of optimal hedge ratios. Second, an out-of-sample test is considered while most studies use only in-sample tests. Third, this thesis is the first to use discontinuous sample periods to separate market conditions and to analyze hedging performance in bull and bear markets.

Author: Francois Duc
Publisher: John Wiley & Sons
ISBN: 0470740795
Category : Business & Economics
Languages : en
Pages : 262

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Book Description
This book provides a cutting edge introduction to market risk management for Hedge Funds, Hedge Funds of Funds, and the numerous new indices and clones launching coming to market on a near daily basis. It will present the fundamentals of quantitative risk measures by analysing the range of Value-at-Risk (VaR) models used today, addressing the robustness of each model, and looking at new risk measures available to more effectively manage risk in a hedge fund portfolio. The book begins by analysing the current state of the hedge fund industry - at the ongoing institutionalisation of the market, and at its latest developments. It then moves on to examine the range of risks, risk controls, and risk management strategies currently employed by practitioners, and focuses on particular risks embedded in the more classic investment strategies such as Long/Short, Convertible Arbitrage, Fixed Income Arbitrage, Short selling and risk arbitrage. Addressed along side these are other risks common to hedge funds, including liquidity risk, leverage risk and counterparty risk. The book then moves on to examine more closely two models which provide the underpinning for market risk management in investment today - Style Value-at-Risk and Implicit Value-at-Risk. As well as full quantitative analysis and backtesting of each methodology, the authors go on to propose a new style model for style and implicit Var, complete with analysis, real life examples and backtesting. The authors then go on to discuss annualisation issues and risk return before moving on to propose a new model based on the authors own Best Choice Implicit VaR approach, incorporating quantitative analysis, market results and backtesting and also its potential for new hedge fund clone products. This book is the only guide to VaR for Hedge Funds and will prove to be an invaluable resource as we embark into an era of increasing volatility and uncertainty.

Author: Henrik Hult
Publisher: Springer Science & Business Media
ISBN: 146144103X
Category : Mathematics
Languages : en
Pages : 343

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Book Description
Investment and risk management problems are fundamental problems for financial institutions and involve both speculative and hedging decisions. A structured approach to these problems naturally leads one to the field of applied mathematics in order to translate subjective probability beliefs and attitudes towards risk and reward into actual decisions. In Risk and Portfolio Analysis the authors present sound principles and useful methods for making investment and risk management decisions in the presence of hedgeable and non-hedgeable risks using the simplest possible principles, methods, and models that still capture the essential features of the real-world problems. They use rigorous, yet elementary mathematics, avoiding technically advanced approaches which have no clear methodological purpose and are practically irrelevant. The material progresses systematically and topics such as the pricing and hedging of derivative contracts, investment and hedging principles from portfolio theory, and risk measurement and multivariate models from risk management are covered appropriately. The theory is combined with numerous real-world examples that illustrate how the principles, methods, and models can be combined to approach concrete problems and to draw useful conclusions. Exercises are included at the end of the chapters to help reinforce the text and provide insight. This book will serve advanced undergraduate and graduate students, and practitioners in insurance, finance as well as regulators. Prerequisites include undergraduate level courses in linear algebra, analysis, statistics and probability.

Author: John R. Birge
Publisher: Elsevier
ISBN: 9780080553252
Category : Business & Economics
Languages : en
Pages : 1026

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Book Description
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.

Author: Oleg V. Bychuk
Publisher: John Wiley & Sons
ISBN: 111808537X
Category : Business & Economics
Languages : en
Pages : 322

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Book Description
Identify and understand the risks facing your portfolio, how to quantify them, and the best tools to hedge them This book scrutinizes the various risks confronting a portfolio, equips the reader with the tools necessary to identify and understand these risks, and discusses the best ways to hedge them. The book does not require a specialized mathematical foundation, and so will appeal to both the generalist and specialist alike. For the generalist, who may not have a deep knowledge of mathematics, the book illustrates, through the copious use of examples, how to identify risks that can sometimes be hidden, and provides practical examples of quantifying and hedging exposures. For the specialist, the authors provide a detailed discussion of the mathematical foundations of risk management, and draw on their experience of hedging complex multi-asset class portfolios, providing practical advice and insights. Provides a clear description of the risks faced by managers with equity, fixed income, commodity, credit and foreign exchange exposures Elaborates methods of quantifying these risks Discusses the various tools available for hedging, and how to choose optimal hedging instruments Illuminates hidden risks such as counterparty, operational, human behavior and model risks, and expounds the importance and instability of model assumptions, such as market correlations, and their attendant dangers Explains in clear yet effective terms the language of quantitative finance and enables a non-quantitative investment professional to communicate effectively with professional risk managers, "quants", clients and others Providing thorough coverage of asset modeling, hedging principles, hedging instruments, and practical portfolio management, Hedging Market Exposures helps portfolio managers, bankers, transactors and finance and accounting executives understand the risks their business faces and the ways to quantify and control them.

Author: Tianjiao Gao
Publisher:
ISBN:
Category :
Languages : en
Pages : 39

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Book Description
In this paper, we derive and assess a framework in which a firm's financial environment is an integral part of its hedging decisions. In the framework, the characteristics of firms in the network and their interconnections affect the firm's risk management strategy through impact on contract cost and efficacy of protection. We apply the model to an investment fund's decision making problem for transferring equity risk to a set of banks and obtain its optimal hedging decision based on a risk-return tradeoff analysis. We find hedge costs greatly influence the fund's choice of counterparties for contract: the cost advantage of a counterparty would award it a dominant role in the magnitude of protection sought from the counterparty. In the a posteriori analysis, we evaluate the hedge efficacy in terms of the counterparties' ability to honor the hedge contract. We investigate counter-party risk by introducing network-caused default probability and recovery rate to our model. We find that the objective and measures used for corporate risk management decide the optimality of hedge contract in the a posteriori analysis. Firms focusing on minimizing variance of firm value might consider a small deviation from the a priori optimal strategy; while those focussed on tail risk tend to stay with the a priori optimal strategy.