Measuring Risk Structures of Assets : P-Index and C-Index

Risk can be defined as the likelihood that you can deliver your promise. This paper has used the European put option and the European call option to construct the p-index and c-index to measure the risk levels (likelihoods) of owning or short-selling an asset when the asset provides at least δ rate of return. The p-index measures the insurance fees for each insured dollar so that the asset can deliver at least δ rate of return. The c-index measures the insurance fees for each dollar of the insurance deductible if the asset delivers at least δ rate of return. It shows that higher p-index means higher c-index. In the binomial case with up move and down move, (1) assets having lower down move have higher p-index, i.e., higher risk for owning the assets; and (2) assets having higher up move have higher c-index, i.e., higher risk for short-selling the assets. The trinomial example however shows that the rankings of risk levels of assets’ providing different rates of returns could reverse