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The limitations of no-arbitrage arguments for real options

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We consider an option c which is contingent on an underlying (tilde S) that is not a traded asset. This situation typically arises in the context of real options. We investigate the situation when there is a "surrogate" traded asset S whose price process is highly correlated with that of (tilde S). An illustration would be the cases where S and (tilde S) model two different brands of crude oil. The main result of the paper shows that in this case one cannot draw any non-trivial conclusions on the price of the option by only using no arbitrage arguments. In a second step we try to isolate hedging strategies on the traded asset S which minimize the variance of the hedging error. We show in particular, that the naive strategy of simply replacing (tilde S) by S fails to be optimal and we are able to quantify how far it is from being optimal. (author's abstract) ; Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

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Friedrich Hubalek, Walter Schachermayer

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