postRisk and skew in options – ponder this

Options are financial products, the premiums of which reflect the likelihood of that option expiring in-the-money at expiry. While this is at best a mathematical deduction, the sheer magnitude of premium will reveal the risk and reward adopted.

Despite the assistance of mathematical models, a trader ought to always understand the basis upon which the model operates and the probabilities associated with each option relative to one another.

If for instance an at-the-money call option is priced at approximately 40 points, intuitively, an in-the-money call options will be worth greater than 40 points, and an out-of the-money call will be worth less than 40 points. Pure premium awareness, along with the parallel delta value of each option ought to become a second nature arrow in the quiver of every productive option trader. When puts and calls are both able to be recognized for what they actually represent; probability and chance, a trader is in command of their environment.

If this is indeed within the grasp of an option trader, whenever they are confronted with an asset, it will not be difficult to immediately recognize anomalies in its derivative option pricing. Indeed the first confirmation that will be made is with the parameters of the underlying assets own pricing.

If the asset is one that has the practical effect of having unlimited scope to experience priced movement in both directions, one can safely assume that out-of-the-money puts and out-of-the-money calls that are equidistant from where the market is at present, will reflect the same probability, and therefore the same delta, and of course the same premium. However, when the asset is a stock price or index price, the ramifications of the above instance are quite different. A stock price by definition cannot have an unlimited range of motion in both directions, for its downside is limited to zero.

This will necessarily place a restriction on the probability of out-of the-money puts as the possibility of a stock price reaching zero or thereabouts certainly exists, by the very nature of asset worth, it is envisaged that an asset will usually be worth something. For this reason puts and calls will be imbued with a distinct skew in price.

In addition to this curiosity, interest rates will play a large part in the fabrication of a stock price call option. While a call option on a stock is available, the comparison will continue to be made between call ownership and outright stock ownership. If the call can be purchased instead of the stock, an upward and favorable move will be experienced by both investments. Often an outright long position in the stock can be replicated precisely in the option market, and it is then that the cost of funding becomes relevant. When the option can be purchased and exercised once it is in-the-money to take advantage of an imminent dividend declaration, an arbitrage would exist if the cost of funding the transaction afforded any advantage to the option investment. Arbitrage opportunities it will be found are quickly exploited and anomalous prices are brought back into line.

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