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Delta, Gamma, Theta, Vega and Rho - you are likely to hear these "Greek" risk measures whenever traders talk about options. Although these terms sound complicated, they actually are easy to understand once you grasp a few basic concepts. Mastering them will give you a good understanding of why options behave the way they do under different circumstances.

Delta - Based on the Odds


Delta or Change per Point is the option's sensitivity to a small change in the stock. For instance, if the stock moves by $0.10 and the option changes by $0.05, then the option is said to have a Delta of 50, meaning that it in dollar terms it matches 50% of a the move in the stock. Conceptually, Delta is related to the probability that an option will end up in-the-money. In the top two parts of Table 1, we show premiums and the Deltas at various stock prices of a call with a $100 strike price and with different lengths of time to go before expiration: 182 days, 91 days and just five days to go before expiration.

Looking at Table 1, notice that with only five days to go, if the stock price is $80, the Delta of the $100 strike call is 0. This is because there is virtually zero likelihood that the call will end up above $100 - i.e. in-the-money.

If the stock price is $120, then the Delta is equal to 100, since there will be a virtual 100% likelihood that the option will stay in-the-money (i.e. end up above $100).

Finally, if the stock price equals $100 shortly before expiration, then the Delta will be close to 50. This is because there is 50% change that the stock will end up in-the-money and a 50% chance that it will end up out-of-the-money.

Now look at the call with 182 days to go. Notice that with the stock at $100, the odds are still reasonably close to 50/50. However, if the stock is equal to $80, the odds will be greater than zero - in this case 35% - that the stock could end up above $100. Alternatively, if the stock is at $120, the 80 Delta is generated by the 80% probability that the stock will end up above $100.

You can easily translate Delta into dollars. Here is an example: if you are long a call on 100 shares of stock priced at $100 (total underlying stock value $10,000) and the Delta is 50, then your equivalent position is $5,000 worth of the stock (or 50 shares).

Gamma: How Quickly the Odds Change


Change in Delta is known as Gamma. It depends on how quickly the odds that the stock will end up in-the-money are likely to change. When an option is deep in-the-money or far out-of-the-money, a small change in the stock price is not likely to change these odds by very much. However, if the option is at-the money options and close to its expiration, then these odds on ending up in-the-money can change very rapidly.

Simple rule of thumb: for the same expiration, at-the-money options have the highest Gamma, while options that are far out-of-the money or deep in-the-money will have lower Gamma.

Looking at the Gamma section of Table 1, notice that the at-the-money $100 strike call with five days to expiration has a Delta of 51 and a Gamma of seven. This means that if the stock moves up by 1%, the Delta is expected to rise by seven, to 57%.

Options with high Gamma will cost more in terms of daily time premium (as a percent of the stock) than will options with low Gamma. This is because you are paying for insurance against the odds changing quickly. Notice that for an at-the-money call with 182 days to go, the Gamma is only one. In our service, Gamma is reported as the expected change in Delta for a 1% change in the stock.

Theta: Paying for Gamma

The daily cost of owning an option is known as its "Time Decay" or Theta. In effect, it is the daily cost of insurance against uncertainty. The quicker the odds change, the greater your uncertainty and the higher will be the Gamma and the Theta of your option. Thus, at the- money options that are close to expiration tend to have the highest Theta, while those with longer maturities tend to have lower Theta. In our service, Theta is expressed in dollars of expected one-day time decay on a 100-share option position. Looking at Table 1, notice that the at-the-money 182-day call has a Theta of $4.19, while the five-day option has a Theta of $24.46. Option buyers should know what it costs per day to own an option, while option writers should know what their current daily rate of accrual is for assuming the risk of the option.

Vega: Exposure to Volatility

Vega is the term for an option premium's exposure to a one percentage point change in implied volatility. (Implied volatility is the volatility number needed to generate a particular premium when all of the other variables, such as stock and strike price, are known.) Notice that the 182-day at-the-money call has a Vega of $27.34. That means that if the implied volatility of the call were to rise from 52% to 53%, the premium on a 100-share option position would rise by $27.34 from $1,500 to $1,527.34. Vega can work very much in your favor if you own a longer-term option and the implied volatility rises. It can work against you heavily, however, if this volatility declines. Therefore with longer-term options, it is important to know whether an option is underpriced or overpriced, since the can quickly expand or contract even if the stock doesn't move.

Rho: Sensitivity to Interest Rates

In our service, we report Rho as the sensitivity of an option on 100 shares to a one percentage point rise in interest rates. To understand Rho, you need to know that, with an option, the underlying price is really the future delivery price of the stock. This future delivery price is determined by the stock price, interest and dividend (if any) and the maturity of the contract. Basically, to hedge an option, the market maker must borrow the funds at the going interest rate to buy the stock. This adds to the underlying price. In addition, to be competitive, the market maker needs to deduct future dividends. Thus, a rise in the interest rate will make the effective price of the underling higher. This will, in turn, cause call premiums to rise and put premiums to decline. Notice in Table 1, that, Rho is higher for the options with the longer maturities and also higher for calls that are in-the-money.

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