When Does Extra Risk Strictly Increase the Value of Options?
2007, Review of Financial Studies
Eric Bennett Rasmusen
It is well known that risk increases the value of options. This paper makes that precise in a new way. The conventional theorem says that the value of an option does not fall if the underlying option becomes riskier in the conventional sense of the mean-preserving spread. This paper uses two new definitions of ``riskier'' to show that the value of an option strictly increases (a) if the underlying asset becomes ``pointwise riskier,'' and (b) only if the underlying asset becomes ``extremum riskier.''.
Rasmusen, Eric, Bennett (2007), "When Does Extra Risk Strictly Increase the Value of Options?" The Review of Financial Studies, 20(5) September, 1647-1667.