## Product Description

Buying The Optimal Moneyness by Giorgos Siligardos, PHD

The market is ready to make a move. You feel it. You see it. It is time to buy options. What moneyness will you choose? In, at, or out? Here’s part 1 of 2.

he first time we encounter the derivatives market, we are fascinated about the potential of big and quick profits buying out-of-the-money (OTM) options and selling them before expiration. Soon we discover that there are times when although we may be correct about the market trend, we nevertheless lose money. Even if we make money, we wonder if we could have better results using options of other “moneyness.”
In this first part of two, I will try to present in a clear and methodical way the three main forces applied to option prices when the underlying instrument moves in the options’ favor. I will explain the deficiencies of the classic sensitivity gauges — delta, vega, and theta — with regard to the practical aspects of option trading for the non–market makers, and employ the elasticity, %vega and %theta functions, for a clearer understanding of these forces.

ON STOCK MARKET INDEX OPTIONS

Unless stated otherwise, all options mentioned are considered European with a stock market index as their underlying. Such options are liquid (and consequently more fairly priced than simple stock options) and perfect for simple modeling purposes (due to absence of dividends and early execution concerns).

DELTA TO MEASURE SENSITIVITY

The simplest greek is delta. Delta measures the sensitivity of an option to a change in its underlying instrument. For example, a delta of 0.3 roughly means that a $1 change in the underlying results in a $0.30 change in the price of the option. In Figure 1, you can see the textbook graphs of the fair prices of European calls and puts along with their corresponding deltas. Judging from Figure 1, the in-the-money (ITM) options have absolute deltas closer to 1, which makes them closely related to the underlying, and OTM options have deltas closer to zero, so they are insensitive to small changes of the underlying.

Though true, this is somehow misleading for our purposes because delta does not measure sensitivity in percentage terms, even though the trading performance is measured that way. If you have an ITM call that costs $40 and an OTM call that costs $5 and their deltas are 0.9 and 0.2, respectively, then a $1 increase in the price of the underlying results in $40.90 (a 2.25% rise in price) and $5.02 (a 4% rise in price) for the ITM and OTM calls. The ITM call gained more in absolute terms, but the OTM call gained more in percentage terms. Had you paid $40 to buy one ITM call, you would gain $0.90. Had you paid the same $40 to buy eight OTM calls, you would gain eight times $0.20, which is $1.60.

SEMILOGARITHMIC CHARTS OF FAIR VALUES

Instead of looking at arithmetic charts for fair values, it is more indicative to look at semilogarithmic charts. In the upper charts of Figure 2, you can see the fair values of options in semilogarithmic charts (the y-axis is logarithmically scaled to show changes from a percentage perspective). You can see that the OTM options are more sensitive in percentage terms than the ITM options are to momentary trends of the underlying.