Options Greeks: Vega Risk and Reward
by John Summa (Contact Author  Biography)When an option is purchased or option strategy established, any price movement of the underlying depending on position Delta will have an impact (unless it is Delta neutral) on the outcome in terms of profit and loss, as was seen in the previous segment of this tutorial. But another important risk/reward dimension exists, usually lurking in the background, which is known as Vega. Vega measures the risk of gain or loss resulting from changes in volatility.
Figure 4: IBM Vega values across time and along strike chains. Values taken on Dec. 29, 2007 with price of underlying at 110.09. 
Source: OptionVue 5 Options Analysis Software 
Figure 4 shows all Vega values as positive because they are not here reflecting position Vegas. Vega for all options is always a positive number because options increase in value when volatility increases and decrease in value when volatility declines. When position Vegas are generated, however, positive and negative signs appear, which are not shown in Figure 4. When a strategist takes a position selling or buying an option, this will result in either a negative sign (for selling) or positive sign (for buying), and the position Vega will depend on net Vegas. What should be obvious from Figure 4 and from the other Vega values is that Vega will be larger or smaller depending on the size of time premium on the options. Time values are viewable in the righthand data column in each month's options window. For the January 110, 105 and 100 calls, for instance, the time values are and 3.01, 1.27 and 0.49 respectively. These higher time premium values are associated with higher Vega values. The 110 strike has Vega of 10.5, the 105 strike a Vega of 8.07 and the 100 a Vega of 4.52.Any other sequence of time value and Vega values in any of the months will show this same pattern. Vega values will be higher on options that have more distant expiration dates . As you can see in Figure 4, for example, the atthemoney call option Vegas (highlighted in yellow), go from 10.5 (January) to 32.1 (July). Clearly, an atthemoney July call option has much greater Vega risk than a January atthemoney call option. This means that LEAPS options, which have sometimes two to three years of time value, will carry very large Vegas and are subject to major risk (and potential reward) from changes in implied volatility. But a distant option with little time premium because it is very far out of the money may have less Vega risk. (For more, see ABCs Of Option Volatility.)The premium for each of these options in the bull call spread is indicated at the left of the yellow highlighted Vega values. You would pay 10.58 ($1,058) and collect 6.36 ($636) for the 100 and 105 January calls, respectively. Since these are inthemoney options, most of the value is intrinsic (IBM price at this snapshot is 110.09).Depending upon whether the strategy employed is Vega long or short, the relationship between price movement and implied volatility can lead to either gains or losses for the options strategist. Let's take a look at a simple example to illustrate this dynamic before exploring some more advanced concepts related to Vega and position Vega.The implied volatility (IV) of options on the S&P 500 index is inversely related to movement of the underlying index. If the market has been bearish, typically IV levels will trend higher and vice versa. Therefore, when a call option is purchased near market bottoms (when IV is at a relatively high level), it is exposed to a negative (inverse) pricevolatility relationship. Buying a call, or any option for that matter, puts you on the long side of Vega (long Vega), which means if IV declines, other things remaining the same, the option strategy will lose. In this example, however, other things don't remain the same, since the market is going to make a bottom and trade higher off that bottom. Delta has a positive impact (the position is long Delta), but this will be offset to the degree Vega, long position Vega and volatility decline. If the market does a Vlike bottom, there is little risk from Theta, or time value decay, since the market moves fast and far, leaving little room for Theta to pose any risk. There are some exceptions, such as bullish call spreads that are inthemoney, or partially inthemoney. For example, if we create a bull call spread to play a market rebound, it would be better from the Vega risk perspective to select a long call that has a smaller Vega value than the one we sell against it. For example, looking at Figure 5, in January, the purchase of an IBM 100 in that month will add long (positive) 4.52 Vegas (here meaning that for every point fall in implied volatility, the option will lose $4.52). Then if we sell a 105 call in the same month, we add 8.07 short (negative) Vegas, leaving a position Vega of 3.55 (the difference between the two) for this bull call spread. Returning to the construction of this inthemoney bull call spread, if the spread is moved outofthemoney, the position Vega will change from net short to net long. As you can see in Figure 5, if an atthemoney strike is bought for 3.10 ($310), it adds 10.5 long Vegas. If the 120 January call is sold for 0.30 ($30) to complete the construction of this at to outofthemoney bull call spread, 4.33 short Vegas are added (remember sold options always have position Vegas that are negative, meaning they benefit from a fall in volatility), leaving a position Vega on the spread of +6.17 (10.5  4.33 = 6.17). With this spread, a rebound in IBM with an associated collapse in implied volatility levels (remember most bigcap stocks and major averages have an inverse priceimplied volatility relationship), would be a negative for this trade, undermining unrealized gains from being long position Delta. We would be better off using an inthemoney bull call spread because it gets us long Delta and short Vega.
Figure 5: IBM Vega values on each strike of inthemoney bull call spread. Position Vega is positive with 8.07 negative Vegas and +4.52 positive Vegas, leaving a net Vega of 3.55. Values taken on Dec. 29, 2007, with IBM at 110.09. Source: OptionVue 5 Options Analysis Software
If playing a market bottom, novice traders might buy a call or bull call spread. Assuming Theta is not a factor here, in a long call position there would be gains resulting from the position's positive Delta, but losses due to having long Vega. Unless we know the exact Vega and Delta values and the size of the drop in implied volatility associated with the price move (typically large inverse relationship at market bottom reversals), we will not know ahead of time exactly how much will be gained or lost on this position. Nevertheless, we know the fact that rebound reversal rallies typically generate large implied volatility decline, so this clearly is not the best approach.Had the trader purchased a call ahead of the rebound and got the directional call correct, a drop in IV would have erased gains from being long Delta. Not a happy outcome, but an experience that should alert a trader to this potential pitfall.A put option buyer would suffer a worse fate. Since the premium on the option is inflated due to raised levels of IV, a buyer of puts would suffer from being on the wrong side of Delta and Vega given a rebound reversal rally. Buying an expensive put and having the market go against you results in a double dose of trouble – being short Delta and long Vega when the market goes up and IV comes crashing down. Clearly, the best of all possible positions here is a long Delta and short Vega play, which at the simplest level would be a short put. But this would hurt doubly if the market continues to go lower. A more conservative play would be an inthemoney bull call spread as discussed earlier.Figure 6 contains the popular options strategies and associated position Vegas. However, as can be seen from the comparison of an inthemoney bull call spread and an at to outofthemoney bull call spread, where spreads are placed, not just the type of spread, can alter the position Vegas, just as it can alter other position Greeks. Therefore, Figure 6 should not be taken as the final word on the position Vegas. It merely provides position Vegas for some standard strategy setups, not all possible strike selection variations of each strategy.
Strategies  Position Vega Signs 
Long Call  Positive 
Short Call  Negative 
Long Put  Positive 
Short Put  Negative 
Long Straddle  Positive 
Short Straddle  Negative 
Long Strangle  Positive 
Short Strangle  Negative 
Put Credit Spread  Negative 
Put Debit Spread  Positive 
Call Credit Spread  Positive 
Call Debit Spread  Negative 
Call Ratio Spread  Negative 
Put Ratio Spread  Negative 
Calendar Spread  Positive 
Covered Call Write  Negative 
Covered Put Write  Negative 
Figure 6: Position Vega signs for common options strategies. The position Vegas in this table represent standard strategy setups. When alternative strike selections are made, the position Vegas can invert. 
ConclusionIn this segment Vega is presented by discussing both position Vega and nonposition Vega, and providing a look at Vega horizontally across time and vertically along strike chains for different months. The pattern of Vega values inside this matrix of strike prices is explained. Finally, negative and positive position Vegas for popular strategies are presented in table format.
Options Greeks: Theta Risk and Reward
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