F. Hubalek, W. Schachermayer
International Journal of Theoretical and Applied Finance, Vol. 4 (2001), No. 2, pp. 361-373.
We consider an option c which is contingent on an underlying 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 S~. An illustration would be the cases where S and S~ model two different brands of crude oil. The main result of the paper shows that in this case one cannot draw any nontrivial 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 S~ by S fails to be optimal and we are able to quantify how far it is from being optimal.
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