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

Chang, Kuo-Ping (2023): Measuring Risk Structures of Assets: P-index and C-index.

Abstract

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 � rate of return. The p-index measures the insurance fees for each insured dollar so that the asset can deliver at least � rate of return. The c-index measures the insurance fees for each dollar of the insurance deductible if the asset delivers at least � 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 shortselling the assets. The trinomial example however shows that the rankings of risk levels of assets' providing different rates of returns could reverse.

• Item Type: MPRA Paper
• Language: English
• Keywords: The put-call parity, the p-index, the c-index, risk structures of assets.
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing; G - Financial Economics > G3 - Corporate Finance and Governance > G32 - Financing Policy ; Financial Risk and Risk Management ; Capital and Ownership Structure ; Value of Firms ; Goodwill

References

Chang, Kuo-Ping, 2023, Corporate Finance: A Systematic Approach, Springer, New York. Chang, Kuo-Ping, 2021, “Put Option and Risk Level of Asset,” http://ssrn.com/abstract=3920521. Chang, Kuo-Ping, 2020, “On Option Greeks and Corporate Finance,” Journal of Advanced Studies in Finance 11, 183-193. DOI:10.14505/jasf.v11.2(22).09 Chang, Kuo-Ping, 2015, The Ownership of the Firm, Corporate Finance, and Derivatives: Some Critical Thinking, Springer, New York. Cox, John, Stephen Ross, and Mark Rubinstein, 1979, “Option Pricing: A Simplified Approach,” Journal of Financial Economics 7, 229-263.