# Delta gamma rho theta vega options trading

Why should you be able to reap even more benefit than if you owned the stock? Calls have positive delta, between 0 and 1. That means if the stock price goes up and no other pricing variables change, the price for the call will go up. If a call has a delta of. Puts have a negative delta, between 0 and That means if the stock goes up and no other pricing variables change, the price of the option will go down.

For example, if a put has a delta of -. As a general rule, in-the-money options will move more than out-of-the-money options , and short-term options will react more than longer-term options to the same price change in the stock.

As expiration nears, the delta for in-the-money calls will approach 1, reflecting a one-to-one reaction to price changes in the stock. As expiration approaches, the delta for in-the-money puts will approach -1 and delta for out-of-the-money puts will approach 0. Technically, this is not a valid definition because the actual math behind delta is not an advanced probability calculation.

However, delta is frequently used synonymously with probability in the options world. Usually, an at-the-money call option will have a delta of about. As an option gets further in-the-money, the probability it will be in-the-money at expiration increases as well. As an option gets further out-of-the-money, the probability it will be in-the-money at expiration decreases.

There is now a higher probability that the option will end up in-the-money at expiration. So what will happen to delta? So delta has increased from. So delta in this case would have gone down to. This decrease in delta reflects the lower probability the option will end up in-the-money at expiration. Like stock price, time until expiration will affect the probability that options will finish in- or out-of-the-money.

Because probabilities are changing as expiration approaches, delta will react differently to changes in the stock price. If calls are in-the-money just prior to expiration, the delta will approach 1 and the option will move penny-for-penny with the stock. In-the-money puts will approach -1 as expiration nears. If options are out-of-the-money, they will approach 0 more rapidly than they would further out in time and stop reacting altogether to movement in the stock.

Again, the delta should be about. Of course it is. So delta will increase accordingly, making a dramatic move from. So as expiration approaches, changes in the stock value will cause more dramatic changes in delta, due to increased or decreased probability of finishing in-the-money.

But looking at delta as the probability an option will finish in-the-money is a pretty nifty way to think about it. As you can see, the price of at-the-money options will change more significantly than the price of in- or out-of-the-money options with the same expiration. Also, the price of near-term at-the-money options will change more significantly than the price of longer-term at-the-money options.

So what this talk about gamma boils down to is that the price of near-term at-the-money options will exhibit the most explosive response to price changes in the stock. But if your forecast is wrong, it can come back to bite you by rapidly lowering your delta. But if your forecast is correct, high gamma is your friend since the value of the option you sold will lose value more rapidly. Since most of these ratios are represented by Greek letters—delta, gamma, theta, and rho—the group is often referred to simply as the greeks.

Vega is also a commonly used ratio and is also considered a greek, although it is not actually a Greek letter some purists prefer to use the Greek letter tau for vega.

These ratios are used to measure potential changes in the value of an actual portfolio or of test portfolios of options from potential changes in the underlying stock price, volatility, or time until expiration.

The delta ratio is the percentage change in the option premium for each dollar change in the underlying. Note that a put option with the same strike price will decline in price by almost the same amount, and will therefore have a negative delta. Options are frequently used to hedge risk. But what if earnings are less than what the market expected.

Then the price may drop a few dollars, resulting in a loss. Therefore, you would want to buy 2 put contracts to cover or hedge your position. Since the value of the portfolio doesn't change within a narrow range, it is said to be delta neutral.

This technique is also called delta hedging. The delta of a portfolio, which is calculated by summing the deltas of each option in the portfolio, is sometimes called its position delta. Delta is also used as a proxy for the probability that a call will expire in the money.

However, delta does not measure probability per se. Delta can serve as a proxy for the probability only because both delta and the probability that a call will go or stay in the money increases as the option goes further into the money. However, delta is not a direct measure of the probability. As an example of where delta and probability will diverge is on the last trading day of the option. Most of the value of a call will depend on the intrinsic value, which is the amount that the underlying price exceeds the strike price of the call.

The above example will not work out perfectly in the real world. You may even ask, why adopt a delta neutral portfolio when your objective is to make a profit? A delta neutral portfolio is only delta neutral within a narrow price range of the underlying. Delta itself changes as the price of the underlying changes. Then you would profit from the puts, but lose on the stock.

So would the profit from the puts completely neutralize the loss on the stock. Actually, you would do better. This results because delta itself changed. Gamma is the change in delta for each unit change in the price of the underlying. The absolute magnitude of delta increases as the time to expiration of the option decreases, and as its intrinsic value increases. Gamma changes in predictable ways. 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 less than 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.

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. Options are a wasting asset.