TAKING A TRADE
A trading opportunity arises when the market price of the option deviates from its fair value — that is, the value that implies zero profit for both buyers and sellers. We assume that trading opportunities are inherent to combinations for which the absolute difference between market and fair values exceeds 1%. The relative frequency of such combinations reflects the abundance of potential trading opportunities existing in the market at a specific time moment.
“Trading opportunities” (above) shows that in crisis, potential trading opportunities exceed those in a calm market. As expiration approaches, the number of trading opportunities falls sharply. However, during the crisis, the rate of this decrease is not as high as during the calm period. Close to expiration, the number of opportunities existing during the crisis is greater than those in the calm period. Also, far from the expiration, the difference between trading potentials is negligible.
Thus, when expiration approaches, more unfairly priced combinations arise during the crisis. Does it mean that the criterion used to reveal potentially profitable combinations would allow identifying these additional trading opportunities, which could raise the number of profitable combinations. Analyzing the criterion effectiveness will answer this.
Several valuation methods should be applied to investigate the impact of the crisis on criterion effectiveness. We begin with ranking analysis developed on the basis of the set theory. This method is based on calculation of the coefficient of the criterion effectiveness k:
k=KP X B/K X P
In the above, B is the total number of combinations (500 in this study, which is the number of straddles in every portfolio), K is the number of combinations with expected profit higher than 1% of the current underlying asset price, P is the number of combinations with profit realized at expiration that is higher than 1% of the current underlying asset price, KP is the number of combinations included in both K and P sets (those of the profitable combinations which were correctly identified by the criterion at the stage of portfolio creation).
The criterion is considered to possess a forecasting capacity when k value exceeds 1. The higher the value of this coefficient, the more effective is the criterion.
“Ranking analysis” shows that the criterion used in this study does not allow benefiting from the sharp rise in the number of trading opportunities occurring during the crisis. While near expiration, the number of trading opportunities is much higher during the crisis than during the calm period, the criterion based on mathematical expectation and on lognormal distribution is more effective in a quiet market. However, when this criterion is applied far from expiration, it shows the same effectiveness regardless of the market phase. In both market environments, the criterion effectiveness is highest close to expiration and decreases sharply as the time to expiration increases.
Ranking analysis of criterion effectiveness estimates the relationship between different combination sets. This method is based on relative frequencies and omits absolute profits of separate combinations. This drawback can be compensated for by considering deviations of actual profits from their expected values and by using correlations between criterion and profit values.
The difference between expected and realized profits increases as the interval between portfolio creation and expiration widens. Such direct relationship is evident both during calm and crisis periods. However, during the crisis, the divergence of two profits increases at a higher rate (see “Deviations from reality,” above). Positive difference means that potential profitability of a combination was overestimated. Negative difference implies that the criterion underestimated the potential profit.