Option Trading Pricing 
Option Delta And Option Theta Explained

The ancient Greeks are justly praised for inventing much of elementary mathematics. But it was left to moderns to create the tools that help options traders quantify risk and calculate prices. Chief among these tools are The Greeks: delta, theta, gamma and vega.

While the underlying mathematics is heavy going, the basic concepts are simple and can be used by any option trader to help measure option trading risk and maximize profits.

The Greeks are based on factors that common sense would suggest affect the price of an option. The determinants are the underlying asset's market price, the option strike price, the time left to expiration, volatility and short-term interest rates. All these pieces of data are readily available and it's clear why they would affect an option's value.

Take the option strike price for example. That's the contractually specified price at which the asset, say a stock, would have to be bought or sold if the stock option were exercised.

Suppose AAPL (Apple) were selling at $188 per share and the option considered was a July 190 call option. (Note: the '190' refers to the option strike price, not the date on which the option expires.) This option is 'out-of-the-money' (OTM) since the strike price is higher than the current market price.

Clearly, the price of the option itself (the 'premium') will be affected by just how far out-of-the-money the option is. One measure of this difference is the first Greek: delta.

Not a simple difference, the delta is a ratio which compares the change in price of the asset to the change in price of the option. For example, if the delta in the above example were 0.52, for every $1 rise in AAPL the call option can be expected to increase by 52 cents ($0.52).

An option trader doesn't need to know how to calculate it, only how to use it. (Any good options trading software will show all four Greeks, along with option strike price, expiration, etc.) Option delta tends to increase the closer the option is to expiration for those close to in-the-money. Option Delta is also affected by changes in implied volatility. (The latter is also frequently provided by option trading software.)

Option Theta measures what is sometimes referred to as the 'time decay' of an option. Since all have an expiration date, and since the less time left the less likely the market price will move in a desired direction, option theta is a measure of option risk and option value.

Suppose that AAPL July 190 call option was priced at $10.75 and the theta was 0.2. Then, in theory, the value of the option would drop by 20 cents ($0.20) per day.

As expiration nears, the price for a premium can be expected to decline at a faster rate. An option with, say, three days left is losing value quicker than one with three months remaining. That change is reflected in the value of option theta.


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