Put Option and Risk Level of Asset

This paper defines an asset’s risk as the likelihood that the asset can deliver at least a specific rate of return. Every asset which provides uncertain payoff has a corresponding put-call parity. The paper uses put option to construct the p-index to measure risk levels (likelihoods) of asset’s providing various rates of return, i.e., risk structure of asset. It shows that in the binomial case with up move and down move, (1) assets having lower down move have higher p-index, i.e., higher risk; (2) all call options have the same p-index, i.e., the same risk level, and all put options have the same p-index; and (3) underlying asset may be riskier than its put option and may have the same risk level as its call option. The trinomial example shows that the ranking of risk levels of assets’ providing different rates of returns could reverse. In the Black-Scholes-Merton model, assets having higher volatility have higher risk.