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Since options and other trading instruments have a variety of risk exposures that can vary dramatically over time or as markets move, it is essential to understand the various risks associated with each trade you placeThe Other Greeks To create a delta neutral trade, you need to select a calculated ratio of short and long positions that combine to create an overall position delta of zero. To accomplish this goal, it is helpful to review a variety of risk exposure measurements. The option Greeks are a set of measurements that can be used to explore the risk exposures of specific trades. Since options and other trading instruments have a variety of risk exposures that can vary dramatically over time or as markets move, it is essential to understand the various risks associated with each trade you place. DEFINING THE GREEKS Options traders have a multitude of different ways to make money by trading options. Traders can profit when a stock price moves substantially or trades in a range. They can also make or lose money when implied volatility increases or decreases. To assess the advantage that one spread might have over another, it is vital to consider the risks involved in each spread. When making these kinds of assessments, options traders typically refer to the following risk measurements: delta, gamma, theta, and vega. These four elements of options risk are referred to as the option Greeks. Lets take a deeper look at the most commonly used Greeks and how they can be used in options trading. First, I would like to go over a couple of technical issues in regard to the Greeks. These numbers are calculated using higher-level mathematics and the Black-Scholes option pricing model. My objective is not to explain those computations, but to shed some light on the practical uses of these concepts. Additionally, I would suggest using an options software program to calculate these numbers so that you are not wasting precious time on tedious mathematics. Lastly, it is important to realize that these numbers are strictly theoretical, meaning that model values may not be the same as those calculated in real-world situations. Each risk measurement (except vega) is named after a different letter in the Greek alphabetdelta, gamma, and theta. In the beginning, it is important to be aware of all of the Greeks, although understanding the delta is the most crucial to your success. Comprehending the definition of each of the Greeks will give you the tools to decipher option pricing as well as risk. Each of the terms has its own specific use in dayto-day trading by most professional traders as well as in my own trading approach. Delta. Change in the price (premium) of an option relative to the price change of the underlying security. Gamma. Change in the delta of an option with respect to the change in price of its underlying security. Theta. Change in the price of an option with respect to a change in its time to expiration. Vega. Change in the price of an option with respect to its change in volatility. Each of these risk measurements contains specific important trading information. As you become more acquainted with the various aspects of options trading, you will find more and more uses for each of them. For example, they each make a unique contribution to an options premium. The two most important components of an options premium are intrinsic value and time value (extrinsic value). In an effort to understand the elements that influence the value of an option, various option pricing models were created, including BlackScholes and Cox-Rubinstein. To comprehend the Greeks, we must understand that they are derived from these types of theoretical pricing models. The values that are needed as inputs into the option pricing models are related to the Greeks. However, the inputs for the models are not the Greeks themselves. A common mistake among options traders is to refer to vega as implied volatility. When we refer to the Greeks, we are talking about risk that will ultimately affect the options price. Therefore, a more accurate description of vega would be the options price sensitivity to implied volatility changes. Delta The concept of the options delta seems to be the first Greek that everyone learns. Its basically a measure of how much the value of an option will change given a change in the underlying stock. When the strike price of the option is close or at-the-money, the delta of the option will be around 50 for long call options and -50 for long put options. In the case of a call option, the options delta could be higher if the value of the stock has exceeded the options strike price significantly. If our call options strike price were much higher than the price of the shares, the value of the delta would be smaller. For example, if XYZ stock is trading for $50 per share and I own the $60 strike price call, my delta may be around 30. Recall that delta is computed using an option pricing model. It will vary based on the difference between the stock price and the strike price of the option as well as the time left until expiration. In this case, lets assume the delta of this option is 30, or .30. Therefore, my position will theoretically make $30 for every $1 increase in XYZ stock based on the options delta. There are many ways that traders can use the delta, or hedge ratio, in their options analysis. A very basic way to use delta is in hedging a shares position. Lets suppose that I have 500 shares of XYZ and that I want to purchase some puts to protect my position. Most traders would purchase five at-the-money puts. This creates a synthetic call position. The idea is that the trader can exercise the puts if the market moves against him. In this respect the purchased options become like insurance for the stock trader. However, there is another way to look at this scenario. If I have 500 shares of XYZ stock, I can hedge the delta of the stock by purchasing 10 of the XYZ at-the-money puts. Since the delta of each share of stock is 1 and the delta of each at-the-money put is -50, I would need 10 puts to hedge the deltas of the long stock position. The results are similar to a straddle. Gamma Gamma tells us how fast the delta of the option changes for every 1 point move in the underlying stock. For this reason, some traders refer to gamma as the delta of the delta. However, gamma is different from delta in that it is always expressed as a positive number regardless of whether it relates to a put or a call. If the price of the stock increases $1 and the delta increases or decreases by a value of 15 then the gamma is 15. Remember, we are using our option pricing model to make this determination. Another interesting characteristic of gamma is that it is largest for the at-themoney options. This means that the deltas for the at-the-money options are more sensitive to a change in the price of the underlying stock. While I have been talking about delta and gamma in relation to the underlying stock price, it is important to note that they are also influenced by time and volatility. Statistical (or historical) volatility is a measure of the fluctuation of the underlying stock. As I have already noted, delta is a measure of how the options price will change when the underlying stock changes. Therefore, the delta of the options will be generally higher for a higher-volatility stock versus a lower-volatility stock. This is due to the fact that the stocks volatility and the options delta are related to the movement of the stock. Also, ITM and ATM option deltas fall faster than OTM options as they approach expiration. Theta The theta of an option is a measure of the time decay of an option. Theta can also be defined as the amount by which the price of an option exceeds its intrinsic value. Generally speaking, theta decreases as an option approaches expiration. Theta is one of the most important concepts for a beginning option trader to understand for it basically explains the effect of time on the premium of the options that have been purchased or sold. The less time that an option has until expiration, the faster that option is going to lose its value. Theta is a way of measuring the rate at which this value is lost. The further out in time you go, the smaller the time decay will be for an option. Therefore, if you want to buy an option, it is advantageous to purchase longer-term contracts. If you are using a strategy that profits from time decay, then you will want to be short the shorter-term options so that the loss in value due to time decay happens quickly. Since an option loses value as time passes, theta is expressed as a negative number. For example, an option (put or call) with a theta of -.15 will lose 15 cents per day. As noted earlier, time decay is not linear. For that reason, options with less time until expiration will have a higher (negative) theta than those with only a few days of life remaining. Vega Vega tells us how much the price of the options will change for every 1 percent change in implied volatility. So, if we purchased the XYZ option for $100 and its vega is 20, we can expect the cost of the option to increase by $20 when implied volatility moves up by 1 percent. Vega tends to be highest for options that are at-the-money and decreases as the option reaches its expiration date. It is interesting to note that vega does not share the correlation to the stocks fluctuation that delta and gamma do. This is because vega is dependent on the measure of implied volatility rather than statistical volatility. This is an important distinction for traders who like to trade options straddles. We all know that there is time value associated with the value of an option. The rate at which the options time premium depreciates on a daily basis is called theta. It is typically highest for at-the-money options and is expressed as a negative value. So, if I have an option that has a theta of -.50, I can expect the value of my option to decrease 50 cents per day until the options expiration. This characteristic of the options time premium has particular interest to the trader of credit spreads. ASSESSING THE RISKS As options traders become more experienced with creating spreads, they should become more aware of the types of risks involved with each spread. To reach this level of trading competence, options traders should combine the values of the Greeks used to create the optimal options spread. The result will allow the trader to more accurately assess the risks of any given options spread. Understanding the relative impact of the Greeks on positions you hold is indispensable. Here are six of the more salient mathematical relationships of these Greek variables: 1. The delta of an at-the-money option is about 50. Out-of-the-money op tions have smaller deltas and they decrease the farther out-of-themoney you go. In-the-money options have greater deltas and they increase the farther in-the-money you go. Call deltas are positive and put deltas are negative. 2. When you sell options, theta is positive and gamma is negative. This means you make money through time decay, but price movement is undesirable. So profits youre trying to earn through option time decay when you sell puts and calls may never be realized if the stock moves quickly in price. Also, rallies in price of the underlying asset will cause your overall position to become increasingly delta-short and to lose money. Conversely, declines in the underlying asset price will cause your position to become increasingly delta-long and to lose money. 3. When you buy options, theta is negative and gamma is positive. This means you lose money through time decay but price movement is desirable. So profits youre attempting to earn through volatile moves of the underlying stock may never be realized if time decay causes losses. Also, rallies in price result in your position becoming increasingly delta-long and declines result in your position becoming increasingly delta-short. 4. Theta and gamma increase as you get close to expiration, and theyre greatest for at-the-money options. This means the stakes grow if youre short at-the-money because either the put or the call can easily become in-the-money and move point-for-point with the equity. You cant adjust quickly enough to accommodate such a situation. 5. When you sell options, vega is negative. This means if implied volatility increases, your position will lose money, and if it decreases, your position will make money. When you buy options, vega is positive, so increases in implied volatility are profitable and decreases are unprofitable. 6. Vega is greatest for options far from expiration. Vega becomes less of a factor while theta and gamma become more significant as options approach expiration. |
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