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Pricing, Hedging and Optimally Designing Derivatives via Minimization of Risk Measures
 IN VOLUME ON INDIFFERENCE PRICING, PRINCETON UNIVERSITY PRESS. 24 BERNARDO A.E. AND LEDOIT O.,(2000
, 2005
"... The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in the literature to provide a satisfactory answer to this probl ..."
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Cited by 56 (5 self)
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The question of pricing and hedging a given contingent claim has a unique solution in a complete market framework. When some incompleteness is introduced, the problem becomes however more difficult. Several approaches have been adopted in the literature to provide a satisfactory answer to this problem, for a particular choice criterion. Among them, Hodges and Neuberger [72] proposed in 1989 a method based on utility maximization. The price of the contingent claim is then obtained as the smallest (resp. largest) amount leading the agent indifferent between selling (resp. buying) the claim and doing nothing. The price obtained is the indifference seller's (resp. buyer's) price. Since then, many authors have used this approach, the exponential utility function being most often used (see for instance, El Karoui and Rouge [51], Becherer [11], Delbaen et al. [39] , Musiela and Zariphopoulou [93] or Mania and Schweizer [89]...). In this chapter, we also adopt this exponential utility point of view to start with in order to nd the optimal hedge and price of a contingent claim based on a nontradable risk. But soon, we notice that the right framework to work with is not that of the exponential utility itself but that of the certainty equivalent which is a convex functional satisfying some nice properties among which that of cash translation invariance. Hence, the results obtained in this particular framework can be immediately extended to functionals satisfying the same properties, in other words to convex risk measures as introduced by FĂ¶llmer and Schied [53] and [54]
Performance of utilitybased strategies for hedging basis risk
 Quant. Finance
"... The performance of optimal strategies for hedging a claim on a nontraded asset is analyzed. The claim is valued and hedged in a utility maximization framework, using exponential utility. A traded asset, correlated with that underlying the claim, is used for hedging, with the correlation typically cl ..."
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Cited by 18 (4 self)
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The performance of optimal strategies for hedging a claim on a nontraded asset is analyzed. The claim is valued and hedged in a utility maximization framework, using exponential utility. A traded asset, correlated with that underlying the claim, is used for hedging, with the correlation typically close to 1. Using a distortion method [30, 31] we derive a nonlinear expectation representation for the claim's ask price and a formula for the optimal hedging strategy. We generate a perturbation expansion for the price and hedging strategy in powers of 2 =1; 2. The terms in the price expansion are found to be proportional to the central moments of the claim payo under a measure equivalent tothephysical measure. The resulting fast computation capability is used to carry out a simulation based test of the optimal hedging program, computing the terminal hedging error over many asset price paths. These errors are compared with those from a naive strategy which uses the traded asset as a proxy for the nontraded one. The distribution of the hedging error acts as a suitable metric to analyze hedging performance. We nd that the the optimal policy improves hedging performance, in that the hedging error distribution is more sharply peaked around a nonnegative pro t. The frequency of pro ts over losses is increased, and this is measured by the median of the distribution, which isalways increased by the optimal strategies. 1