The Limitations of No-Arbitrage Arguments for Real Options

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 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 ~ S by S fails to be optimal and we are able to quantify how far it is from being optimal.