1. But since the Put-Call Parity employs two derivatives, one can be non-redundant and the other can go Missing when an implied redundant price cannot justify an offsetting trade. (Note that this view reflects the bias that a Call option price, for example, on its own is not redundant-a readily justifiable observation and claim.) 6. The PCP formula seems to be applied when not fully needed, and also not justifiable. Namely, the PCP formula is sometimes imposed or invoked when only a Put-Call Equivalency of payouts can be identified. The difference is that conditions for economic valuation and arbitrage requirements are not necessarily met in the application. Sometimes, valuations are imposed on the separate pieces; but when different investors hold the pieces and value them separately, it is difficult to justify that the valuations should be equated. Namely, the Put-Call Valuation concept of parity exists only on an individual basis and cannot be justified when the pieces are split and valued by more than one investor;While the one-derivative Spot-Futures Parity could force the futures price to express a redundant price, rather than express a non-redundant Expectation of the Spot; the two-derivative Put-Call Parity could allow one derivative to be non-redundant and the other to go untraded (i.e
2. S) and one valuation (e.g., a formulaic calculation of a numerical value of C based on an economic valuation process) weakens the argument even more, especially when the "price" that is used cannot be demonstrated to be consistent with the valuation concept used for the other part (e.g., the "price" of S is inconsistent with the valuation concept utilized for C). A more consistent approach for PCV: the Stock could be valued according to the same valuation argument utilized for the Call. The argument also weakens when neither the Derivation nor Portfolio Representation of the PCP formula is used but, rather, an Uncertainty Representation is used. Hence, any broad argument for the use of an implied Put formula;The PCP formula seems to be applied in conditions that weaken its argument. Namely, when "prices" and "values" are mixed, and when an Uncertainty Representation is employed
3. Though Derman (2009) mentions "Resemblance is not enough" (p.29), an accompanying "The law of one price -this valuation by analogy -is the only genuine law in quantitative finance, and it is not a law of nature" (p.31) statement is questionable. The "law of one price" appears to be an analogy that is misapplied toward the PCP. And yet, analogy is not precise enough for (strict) arbitrage. In fact, analogy can lead to where an arbitrage opportunity exists. For example, consider an investor who imposes both (1) a "valuation by analogy" arbitrage model and (2) an "arbitrage will hold the prices tight" assumption. Such a condition is likely where to find a more astute investor arbitraging the investor implementing the model (e.g., consider a central bank attempting to enforce a currency exchange rate.) Loose definitions and illiquidity are enough to kill the applicability of an analogy. Accordingly, "valuation by analogy" can be an example of Bad Creativity for arbitrage-based modelse.g., where bad models lead to misrepresentation. 11. Yet, the PCP is still a valuable heuristic. Even uses for bad models do exist. The PCP does help frame certain problems, and in the process helps outline requisites for the PCP formula to have any inferential power in application. The PCP formula could be used as a viably justified standard (when precision is not needed-as in an accounting standard)-as long as the caveats are identified with respect to such requisites. However, the PCP formula is not necessarily the best heuristic. For example, some research would seem to have benefitted from using only the similar-payout representation of the PCE formula rather than trying to invoke the PCP formula. While the PCE formula requires neither liquidity nor ability to hold, the PCP formula requires both. And yet, the PCE approach is still limited to "different investors will likely value the uncertain parts differently;Hence, it is subject to arbitrage conditions being met, including liquidity, Holdability, and other aspects. PCP formula application misuse reminds us that "limitations of arbitrage" do exist. These examples demonstrate precisely why (and when) arbitrage has a low power of argument. Including why arbitrage concepts cannot and should not be used to either "price" or "value" a stand-alone financial instrument. And if arbitrage cannot hold a simple financial derivative valuation model tight, then would it necessarily be able to hold tight a more-complex financial derivative model? While implied-PCP-formula calculations can represent a "selling" price, or a "completing a hedge, without the hedge premium included" price, they cannot necessarily represent stand-alone values for risk bearing,2011