Efficient hedging: Cost versus shortfall risk

Abstract

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. An investor faced with a contingent claim may eliminate risk by (super-) hedging in a nancial market. As this is often quite expensive, we study partial hedges which require less capital and reduce the risk. In a previous paper we determined quantile hedges which succeed with maximal probability, given a capital constraint. Here we look for strategies which minimize the shortfall risk de ned as the expectation of the shortfall weighted by some loss function. The resulting e cient hedges allow the investor to interpolate in a systematic way b e t ween the extremes of no hedge and a perfect (super-) hedge, depending on the accepted level of shortfall risk. Terms of use: Documents in EconStor may

Option pricing with transaction costs using a Markov chain approximation

“…A further possibility is to consider "coherent" measures of risk, introduced by Artzner et al (1999), and extended to a dynamic setting by and Cvitanià c and Karatzas (1999). One example of such a risk measure is provided by the "shortfall risk" minimisation of F ollmer and Leukert (2000). In general, the interaction between agents' preferences and option prices in incomplete markets is a fertile area for future research, and recent papers addressing this topic include Rouge and El Karoui (2000), Barrieu and El Karoui (2002) and Musiela and Zariphopoulou (2001).…”

Robustness of shortfall risk minimising strategies in the binomial model

“…As a consequence, we decided to follow a "dual" approach (with techniques similar to those in [3]), based on the fact that the problem min α E S0,V0 {(H(S N )−V α N ) + } has the same solution as the "static" problem min X∈X E S0 H(S N )− X , where X := {X | X ≤ H(S N ) (a.s.), E * {X} ≤ V 0 } is the set of the so-called modified contingent claims, i.e., all the claims less than H(S N ) which can be replicated with initial capital (less than or equal to) V 0 . It is then possible to show that the optimal solution of the static problem min X∈X E S0 H(S N ) − X is given by the modified contingent claim X * := H(S N ) − I c * dP * dP , with I := ( ) −1 and c * > 0 chosen in such a way that E * {X * } = V 0 .…”

Portfolio management in the binomial model: conditions for outperforming benchmarks

“…The analysis of this question is implicitly included in the works of Föllmer and Leukert ( [15], [16]) in great generality (cf. [29] in a discrete-time framework).…”

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