Kim also has the alternative to buy an ITM call. Instead of the 35 or 37.50 call, she can buy the 32.50. The 32.50 call shares some of the advantages the 37.50 call has over the 35 call, but its overall greek characteristics make it a very different trade from the two previous alternatives. Exhibit 4.10 shows a comparison of the greeks of the three different calls.Like the 37.50 call, the 32.50 has a lower gamma, theta, and vega than the ATM 35-strike call.
Because the call is ITM, it has a higher delta: 0.862.In this example, Kim can buy the 32.50 call for 3. That’s 0.40 over parity (3 2 [35.10 2 32.50] 5 0.40). There is not much time value, but more than the 37.50 call has. Thus, theta is of some concern. Ultimately, the ITMs have 0.40 of time value to lose compared with the 0.20 of the OTM calls. Vega is also of some concern, but not as much as in the other alternatives because the vega of the 32.50 is lower than the 35s or the 37.50s.Gamma doesn’t help much as the stock rallies—it will get smaller as the stock price rises.
Gamma will, however, slow losses somewhat if the stock declines by decreasing delta at an increasing rate.In this case, the greek of greatest consequence is delta—it is a more purely directional play than the other alternatives discussed. Exhibit 4.11 shows the matrix of the delta of the 32.50 call.Because the call starts in-the-money and has a relatively low gamma, the delta remains high even if Disney declines significantly.
Gamma doesn’t really kick in until the stock retreats enough to bring the call closer to being at-the-money. At that point, the position will have suffered a big loss, and the higher gamma is of little comfort.Kim’s motivation for selecting the ITM call above the ATM and OTM calls would be increased delta exposure. The 0.86 delta makes direction the most important concern right out of the gate. Exhibit 4.12 shows the theoretical values of the 32.50 call.Small directional moves contribute to significant leveraged gains or losses.
From share price $35 to $36, the call gains 0.90—from 2.91 to 3.81—about a 30 percent gain. However, from $35 to $34, the call loses 0.80, or 27 percent. With only 0.40 of time value, the nondirectional greeks(theta, gamma, and vega) are a secondary consideration.If this were a deeper ITM call, the delta would start out even higher,closer to 1.00, and the other relevant greeks would be closer to zero. The deeper ITM a call, the more it acts like the stock and the less its option characteristics (greeks) come into play.
Long ATM Put:The beauty of the free market is that two people can study all the available information on the same stock and come up with completely different outlooks. First of all, this provides for entertaining television on the business-news channels when the network juxtaposes an outspoken bullish analyst with an equally unreserved bearish analyst. But differing opinions also make for a robust marketplace. Differing opinions are the oil that greases the machine that is price discovery.
From a market standpoint, it’s what makes the world go round.It is possible that there is another trader, Mick, in the market studying Disney, who arrives at the conclusion that the stock is overpriced. Mick believes the stock will decline in price over the next three weeks. He decides to buy one Disney March 35 put at 0.80. In this example, March has 44 days to expiration.Mick initiates this long put position to gain downside exposure, but along with his bearish position comes option-specific risk and opportunity.
Mick is buying the same month and strike option as Kim did in the first example of this chapter: the March 35 strike. Despite the different directional bias, Mick’s position and Kim’s position share many similarities.Exhibit 4.13 offers a comparison of the greeks of the Disney March 35 call and the Disney March 35 put.The first comparison to note is the contrasting deltas. The put delta is negative, in contrast to the call delta. The absolute value of the put delta is close to 1.00 minus the call delta.
The put is just slightly OTM, so its delta is just under 0.50, while that of the call is just over 0.50. The disparate, yet related deltas represent the main difference between these two trades.The difference between the gamma of the 35 put and that of the corresponding call is fairly negligible: 0.174 versus 0.166, respectively.The gamma of this ATM put will enter into the equation in much the same way as the gamma of the ATM call.
The put’s negative delta will become more negative as the stock declines, drawing closer to 21.00. It will get less negative as the stock price rises, drawing closer to zero. Gamma is important here, because it helps the delta. Delta, however, still remains the most important greek. Exhibit 4.14 illustrates how the 35 put delta changes as time and price change.