06-03-2009, 05:04 PM
Options are considered a wasted asset because of their limited life. Option premiums can vary quickly with the price and volatility of the underlying asset and time decay of the options contract. Calculations used to identify variables used in calculating an options price are often refer to "the Greeks", especially Delta, Vega, Gamma, and Theta. These are mathematical characteristics of the Black-Scholes model named after the Greek letters used to represent them in equations.
DELTA- Delta measures how much an option price will move relative to the underlying asset. It is the percentage change in the option premium for each dollar change in the underlying option.
Some call it the 'hedge ratio.' For example, say you have a call option with a delta of 0.8, it means for every $1 the stock increases the call option will increase by 80 cents.
Call options said to be 'in the money' as it nears expiration, it will approach a delta of 1.00. When a Call option that is in-the-money put option nears expiration, it will approach a delta of -1.00.
Say a stock has a strike price of $20 and its price goes up $2. This will cause the Call option premium to rise by a certain percentage. Say the price rises $1. The Call option is said to have a positive delta of 50% because the premium increased $1 for a $2 stock price increase. The Put option on the other hand is said to have a negative delta because the Put option should decrease the same amount.
Options are many times used to hedge a position or risk. This is known as hedging risk. If, for instance, you own a 100 shares of a stock priced at $50 and you expect the price to go up after earnings. Once it goes up you may want to lock in your profits. What happens if your stock comes in under estimates? To protect your position how many Puts should you buy to hedge your position? If the delta of the put is -$.50, then the put will increase in value by 50¢ for each $1 drop in the price of the stock, at least while it hovers around the strike price. Therefore, you would want to buy 2 put contracts to cover or hedge your position. If the value of the portfolio doesn’t change within a narrow range, it is said to be delta neutral. The delta of a portfolio is sometimes called its position delta.
GAMMA- Basically the Gamma is the rate of change for delta as it relates to the stock price. Gamma is used to gauge how far an option price is compared to the degree it is in or out of the money.
If the option is deep in or out of the money it typically has a small Gamma. When the option is near or at the money the Gamma is at its largest value. As an option goes more into the money, delta will increase until it tracks the underlying dollar for dollar; however, delta can never be greater than 1, or, in the case of a put, less than -1. When delta is close to 1 or -1, then gamma is near zero, because delta doesn’t change much with the price of the underlying stock.
Gamma and delta are greatest when an option is at the money—when the strike price is equal to the price of the underlying. The change in delta is greatest for options at the money, and decreases as the option goes more into the money or out of the money. Both gamma and delta tend to zero as the option moves further out of the money. The total gamma of a portfolio is called the position gamma.
THETA- Theta measures the time decay in an option, or the amount of money an option will lose each day due to the time passing. Theta is the expected change in option price due to the passage of time. Theta is expressed as the loss of time value per day. Thus, a theta of -.1 indicates that the option is losing $.10 per day.
For at the money options, theta increases as an option approaches the expiration date. Theta is very little for a long-term option, and increases as expiration nears. For in and out of the money options, theta decreases as an option approaches expiration.
Theta is greater for more volatile assets, because volatility increases the option premium by increasing the time value of the premium.
However, because time decay is generally considered to favor the option writer, a short position in options is said to have positive position theta. The net of the positive and negative position thetas is the total position theta of the portfolio.
VEGA- Vega is the sensitivity of the option price to changes in implied volatility. Vega measures the change in the option premium due to changes in the volatility of the underlying stock, and is always expressed as a positive number.
Vega tends to be the greatest when the option is at the money and least when the option is far out of the money or in the money.
Each individual option has its own vega and can react differently to changes in volatility. Vega estimates how much an option price would change when volatility changes 1%. It seems that volatility impacts are greater in the at the money options as opposed to the in or out of the money options. Vega seems to impact calls more than puts. If you look at longer term options such as LEAPS you will see the affect more clearly.
- Long calls and long puts; always have positive vega.
- Short calls and short puts; always have negative vega.
- Stock has zero vega; it’s value is not affected by volatility.
Positive vega- Option price increases when volatility increases, decreases when volatility decreases.
Negative vega-Option price decreases when volatility increases, increases when volatility decreases.
Example:
XYZ March 50 Call is going for $4, with Vega 0.20, volatility of ABC stock is 25%. Say the volatility increases to 26%. XYZ March 50 Call’s price will rise to $4.20. If the volatility drops to 24%, XYZ March 50 Call value drops to $2.80.
Vega falls when volatility drops or the option closes in on expiration. If there is more time left, vega should be higher.
Vega can move sometimes without any changes in the underlying volatility changing. For example, if expectation changes for a stock because of a impending earnings release, or an important news announcement. The vega can also rise quickly when things like a stock market crash or sudden move in a stock price.
Rho- Typically higher interest rates will result in a higher Call premium and lower Put Premiums. Rho is the amount of change in premiums due to a 1% change in the prevailing risk-free interest rate.
DELTA- Delta measures how much an option price will move relative to the underlying asset. It is the percentage change in the option premium for each dollar change in the underlying option.
Some call it the 'hedge ratio.' For example, say you have a call option with a delta of 0.8, it means for every $1 the stock increases the call option will increase by 80 cents.
Call options said to be 'in the money' as it nears expiration, it will approach a delta of 1.00. When a Call option that is in-the-money put option nears expiration, it will approach a delta of -1.00.
Say a stock has a strike price of $20 and its price goes up $2. This will cause the Call option premium to rise by a certain percentage. Say the price rises $1. The Call option is said to have a positive delta of 50% because the premium increased $1 for a $2 stock price increase. The Put option on the other hand is said to have a negative delta because the Put option should decrease the same amount.
Options are many times used to hedge a position or risk. This is known as hedging risk. If, for instance, you own a 100 shares of a stock priced at $50 and you expect the price to go up after earnings. Once it goes up you may want to lock in your profits. What happens if your stock comes in under estimates? To protect your position how many Puts should you buy to hedge your position? If the delta of the put is -$.50, then the put will increase in value by 50¢ for each $1 drop in the price of the stock, at least while it hovers around the strike price. Therefore, you would want to buy 2 put contracts to cover or hedge your position. If the value of the portfolio doesn’t change within a narrow range, it is said to be delta neutral. The delta of a portfolio is sometimes called its position delta.
GAMMA- Basically the Gamma is the rate of change for delta as it relates to the stock price. Gamma is used to gauge how far an option price is compared to the degree it is in or out of the money.
If the option is deep in or out of the money it typically has a small Gamma. When the option is near or at the money the Gamma is at its largest value. As an option goes more into the money, delta will increase until it tracks the underlying dollar for dollar; however, delta can never be greater than 1, or, in the case of a put, less than -1. When delta is close to 1 or -1, then gamma is near zero, because delta doesn’t change much with the price of the underlying stock.
Gamma and delta are greatest when an option is at the money—when the strike price is equal to the price of the underlying. The change in delta is greatest for options at the money, and decreases as the option goes more into the money or out of the money. Both gamma and delta tend to zero as the option moves further out of the money. The total gamma of a portfolio is called the position gamma.
THETA- Theta measures the time decay in an option, or the amount of money an option will lose each day due to the time passing. Theta is the expected change in option price due to the passage of time. Theta is expressed as the loss of time value per day. Thus, a theta of -.1 indicates that the option is losing $.10 per day.
For at the money options, theta increases as an option approaches the expiration date. Theta is very little for a long-term option, and increases as expiration nears. For in and out of the money options, theta decreases as an option approaches expiration.
Theta is greater for more volatile assets, because volatility increases the option premium by increasing the time value of the premium.
However, because time decay is generally considered to favor the option writer, a short position in options is said to have positive position theta. The net of the positive and negative position thetas is the total position theta of the portfolio.
VEGA- Vega is the sensitivity of the option price to changes in implied volatility. Vega measures the change in the option premium due to changes in the volatility of the underlying stock, and is always expressed as a positive number.
Vega tends to be the greatest when the option is at the money and least when the option is far out of the money or in the money.
Each individual option has its own vega and can react differently to changes in volatility. Vega estimates how much an option price would change when volatility changes 1%. It seems that volatility impacts are greater in the at the money options as opposed to the in or out of the money options. Vega seems to impact calls more than puts. If you look at longer term options such as LEAPS you will see the affect more clearly.
- Long calls and long puts; always have positive vega.
- Short calls and short puts; always have negative vega.
- Stock has zero vega; it’s value is not affected by volatility.
Positive vega- Option price increases when volatility increases, decreases when volatility decreases.
Negative vega-Option price decreases when volatility increases, increases when volatility decreases.
Example:
XYZ March 50 Call is going for $4, with Vega 0.20, volatility of ABC stock is 25%. Say the volatility increases to 26%. XYZ March 50 Call’s price will rise to $4.20. If the volatility drops to 24%, XYZ March 50 Call value drops to $2.80.
Vega falls when volatility drops or the option closes in on expiration. If there is more time left, vega should be higher.
Vega can move sometimes without any changes in the underlying volatility changing. For example, if expectation changes for a stock because of a impending earnings release, or an important news announcement. The vega can also rise quickly when things like a stock market crash or sudden move in a stock price.
Rho- Typically higher interest rates will result in a higher Call premium and lower Put Premiums. Rho is the amount of change in premiums due to a 1% change in the prevailing risk-free interest rate.