what are the greeks 
the variables that are used to assess risk in the options market are commonly referred to as the greeks a greek symbol is used to designate each of these risks each greek variable is a result of an imperfect assumption or relationship of the option with another underlying variable traders use different greek values such as delta theta and others to assess options risk and manage option portfolios understanding the greeksgreeks encompass many variables these include delta theta gamma vega and rho among others each one of these greeks has a number associated with it and that number tells traders something about how the option moves or the risk associated with that option the primary greeks delta vega theta gamma and rho are calculated each as a first partial derivative of the options pricing model for instance the black scholes model the number or value associated with a greek changes over time therefore sophisticated options traders may calculate these values daily to assess any changes that may affect their positions or outlook or simply to check if their portfolio needs to be rebalanced below are several of the main greeks traders look at deltadelta represents the rate of change between the option s price and a 1 change in the underlying asset s price in other words the price sensitivity of the option is relative to the underlying asset the delta of a call option has a range between 0 and 1 while the delta of a put option has a range between 0 and 1 for example assume an investor is long a call option with a delta of 0 50 therefore if the underlying stock increases by 1 the option s price would theoretically increase by 50 cents for options traders delta also represents the hedge ratio for creating a delta neutral position for example if you purchase a standard american call option with a 0 40 delta you will need to sell 40 shares of stock to be fully hedged net delta for a portfolio of options can also be used to obtain the portfolio s hedge ratio a less common usage of an option s delta is the current probability that the option will expire in the money for instance a 0 40 delta call option today has an implied 40 probability of finishing in the money thetatheta represents the rate of change between the option price and time or time sensitivity sometimes known as an option s time decay theta indicates the amount an option s price would decrease as the time to expiration decreases all else equal for example assume an investor is long an option with a theta of 0 50 the option s price would decrease by 50 cents every day that passes all else being equal theta increases when options are at the money and decreases when options are in and out of the money options closer to expiration also have accelerating time decay long calls and long puts will usually have negative theta short calls and short puts will have positive theta by comparison an instrument whose value is not eroded by time such as a stock would have zero theta gammagamma represents the rate of change between an option s delta and the underlying asset s price this is called second order second derivative price sensitivity gamma indicates the amount the delta would change given a 1 move in the underlying security for example assume an investor is long on a call option on hypothetical stock xyz the call option has a delta of 0 50 and a gamma of 0 10 therefore if stock xyz increases or decreases by 1 the call option s delta would increase or decrease by 0 10 gamma is used to determine how stable an option s delta is higher gamma values indicate that delta could change dramatically in response to even small movements in the underlying s price gamma is higher for options that are at the money and lower for options that are in and out of the money and accelerates in magnitude as expiration approaches gamma values are generally smaller the further away from the date of expiration options with longer expirations are less sensitive to delta changes as expiration approaches gamma values are typically larger as price changes have more impact on gamma options traders may opt to not only hedge delta but also gamma in order to be delta gamma neutral meaning that as the underlying price moves the delta will remain close to zero read about investopedia s 10 rules of investing by picking up a copy of our special issue print edition vegavega represents the rate of change between an option s value and the underlying asset s implied volatility this is the option s sensitivity to volatility vega indicates the amount an option s price changes given a 1 change in implied volatility for example an option with a vega of 0 10 indicates the option s value is expected to change by 10 cents if the implied volatility changes by 1 because increased volatility implies that the underlying instrument is more likely to experience extreme values a rise in volatility will correspondingly increase the value of an option conversely a decrease in volatility will negatively affect the value of the option vega is at its maximum for at the money options that have longer times until expiration greek language buffs will point out that there is no actual greek letter vega there are various theories about how this symbol which represents the greek letter nu found its way into stock trading lingo rhorho represents the rate of change between an option s value and a 1 change in the interest rate this measures sensitivity to the interest rate for example assume a call option has a rho of 0 05 and a price of 1 25 if interest rates rise by 1 the value of the call option would increase to 1 30 all else being equal the opposite is true for put options rho is greatest for at the money options with long times until expiration minor greekssome other greeks which aren t discussed as often are lambda epsilon vomma vera zomma and ultima these greeks are second or third derivatives of the pricing model and affect things such as the change in delta with a change in volatility and so on they are increasingly used in options trading strategies as computer software can quickly compute and account for these complex and sometimes esoteric risk factors implied volatilityimplied volatility is not a greek but it is related to them this value forecasts how volatile the stock underlying an option will be in the future implied volatility is theoretical meaning it shows what is expected but is not always dependable this value is usually reflected in the price of an option implied volatility can help you judge what assumptions market makers are using to set their bid and ask prices implied volatility is often provided on options trading platforms rather than being something that traders need to calculate for themselves this is because market makers use implied volatility to set their prices so traders need to know how volatile those market makers think an underlying stock will be implied volatility is based on a number of factors including comparing an underlying stock s historic volatility to its implied volatility can help you judge whether the option you are considering is priced low or high if the implied volatility is higher than normal this generally benefits option sellers implied volatility that is lower than normal on the other hand usually benefits option buyers 