Hedging Under Generalized Good-Deal Bounds and Model Uncertainty PDF Download
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Author: Dirk Becherer
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Languages : en
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Book Description
We study a notion of good-deal hedging, that corresponds to good-deal valuation and is described by a uniform supermartingale property for the tracking errors of hedging strategies. For generalized good-deal constraints, defined in terms of correspondences for the Girsanov kernels of pricing measures, constructive results on good-deal hedges and valuations are derived from backward stochastic differential equations, including new examples with explicit formulas. Under model uncertainty about the market prices of risk of hedging assets, a robust approach leads to a reduction or even elimination of a speculative component in good-deal hedging, which is shown to be equivalent to a global risk-minimization in the sense of Föllmer and Sondermann (1986) if uncertainty is sufficiently large.
Author: Dirk Becherer
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We study a notion of good-deal hedging, that corresponds to good-deal valuation and is described by a uniform supermartingale property for the tracking errors of hedging strategies. For generalized good-deal constraints, defined in terms of correspondences for the Girsanov kernels of pricing measures, constructive results on good-deal hedges and valuations are derived from backward stochastic differential equations, including new examples with explicit formulas. Under model uncertainty about the market prices of risk of hedging assets, a robust approach leads to a reduction or even elimination of a speculative component in good-deal hedging, which is shown to be equivalent to a global risk-minimization in the sense of Föllmer and Sondermann (1986) if uncertainty is sufficiently large.
Author: Dirk Becherer
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Languages : en
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Book Description
We derive robust good-deal hedges and valuations under combined model ambiguity about the drift and volatility of asset prices for incomplete markets. Good-deal valuations are determined such that not just opportunities for arbitrage but also for overly attractive reward-to-risk ratios are excluded, by restricting instantaneous Sharpe ratios for any market extension by derivatives. From a finance point of view, this permits for hedges and valuation bounds than are less extreme (respectively expensive) than those from the more fundamental approach of almost-sure superhedging and its corresponding no-arbitrage bounds. In mathematical terms, it demands however that not just ambiguities about the volatility but also about the drift become relevant. For general measurable contingent claims, possibly path-dependent, the solutions are described by 2nd-order backward stochastic differential equations with non-convex drivers, building on recent research progress on non-linear kernels. Hedging strategies are robust with respect to uncertainty in the sense that their tracking errors satisfy a supermartingale property under all a-priori valuation measures, uniformly over all priors.
Author: Samuel N. Cohen
Publisher: Springer Nature
ISBN: 3030222853
Category : Mathematics
Languages : en
Pages : 300
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Book Description
This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.
Author: Michael Kirch
Publisher:
ISBN:
Category :
Languages : en
Pages : 137
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Book Description
Author: Helyette Geman
Publisher: Springer Science & Business Media
ISBN: 3662124297
Category : Mathematics
Languages : en
Pages : 522
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Book Description
The Bachelier Society for Mathematical Finance held its first World Congress in Paris last year, and coincided with the centenary of Louis Bacheliers thesis defence. In his thesis Bachelier introduces Brownian motion as a tool for the analysis of financial markets as well as the exact definition of options. The thesis is viewed by many the key event that marked the emergence of mathematical finance as a scientific discipline. The prestigious list of plenary speakers in Paris included two Nobel laureates, Paul Samuelson and Robert Merton, and the mathematicians Henry McKean and S.R.S. Varadhan. Over 130 further selected talks were given in three parallel sessions. .
Author: Anne Balter
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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Book Description
We search for a trading strategy and the associated robust price of unhedgeable assets in incomplete markets under the acknowledgement of model uncertainty. Our set-up is that we postulate an agent who wants to maximise the expected surplus by choosing an optimal investment strategy. Furthermore, we assume that the agent is concerned about model misspecification. This robust optimal control problem under model uncertainty leads to (i) risk-neutral pricing for the traded risky assets, and (ii) adjusting the drift of the nontraded risk drivers in a conservative direction. The direction depends on the agent's long or short position, and the adjustment that ensures a robust strategy leads to what is known as "actuarial" or "prudential" pricing. Our results extend to a multivariate setting. We prove existence and uniqueness of the robust price in an incomplete market via the link between the semilinear partial differential equation and backward stochastic differential equations.
Author:
Publisher:
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Category :
Languages : en
Pages : 52
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Book Description
Faced with the problem of pricing complex contingent claims, investors seek to make their valuations robust to model uncertainty. We construct a notion of a modeluncertainty-induced utility function and show that model uncertainty increases investors' effective risk aversion. Using this utility function, we extend the "no good deals" methodology of Cochrane and Saá-Requejo (2000) to compute lower and upper gooddeal bounds in the presence of model uncertainty. We illustrate the methodology using some numerical examples. -- asset pricing theory ; good-deal bounds ; Knightian uncertainty ; model uncertainty ; contingent claim pricing ; model-uncertainty-induced utility function
Author: Erhan Bayraktar
Publisher:
ISBN:
Category :
Languages : en
Pages : 28
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Book Description
With model uncertainty characterized by a convex, possibly non-dominated set of probability measures, the investor minimizes the cost of hedging a path dependent contingent claim with given expected success ratio, in a discrete-time, semi-static market of stocks and options. Based on duality results which link quantile hedging to a randomized composite hypothesis test, an arbitrage-free discretization of the market is proposed as an approximation. The discretized market has a dominating measure, which guarantees the existence of the optimal hedging strategy and enables numerical calculation of the quantile hedging price by applying the generalized Neyman-Pearson Lemma. Finally, the performance in the original market of the approximating hedging strategy and the convergence of the approximating quantile hedging price are analyzed.
Author: Takaki Hayashi
Publisher:
ISBN:
Category : Equilibrium (Economics)
Languages : en
Pages : 296
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Author: John B. McDermott
Publisher:
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Category :
Languages : en
Pages :
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We examine the general hedging problem faced by a global portfolio manager or a pure exporting multinational firm. Most hedging models assume that these economic agents hold only a single asset in the spot market and are exposed only to a single source of price-quantity uncertainty. Such models are less relevant to many financial and exporting firms which face multiple sources of risk. In this paper we develop a general hedging model which explicitly recognizes that these hedgers are faced with multiple price and quantity uncertainties. Our model takes advantage of the full correlation structure of changes in spot prices, quantities and forward prices. We carry out simulations of the hedging model for a firm with two pairs of price and quantity exposures to demonstrate potential gains in hedging efficiency and effectiveness.
