A new approximation for the risk premium with large risks

PurposeThe Arrow–Pratt approximation to the risk premium is only valid for small risks. In this paper we consider a second approximation, based on risk-neutral probabilities and which requires no greater information than the Arrow–Pratt approximation, that works well for both small and large risks.Design/methodology/approachThe paper is theoretical in nature, although it also provides illustrative numerical simulations.FindingsThe new approximation proposed here appears to be significantly superior to Arrow–Pratt for approximating the true value of the risk premium when the risk is large. It may also approximate better even for relatively small risks.Originality/valueAs far as we are aware, there are no other known approximations for the risk premium when the risk involved is large.