# Stock Option Pricing and the Greeks

Option Prices Are Effected By Several Factors Called The Greeks, And It Is Critical You Understand What They Are.Options are derivative securities. They derive their value from some underlying security or index and their price is affected by a number of factors. Because of their derivative nature, they behave differently than the underlying security and their price will not necessarily respond as you might first expect.

The primary factors that affect an option’s price include the price of the underlying security, volatility, the time remaining until the option's expiration date, interest rates, and dividends. Anticipating the combined impact of each one of these factors is potentially critical to the success of an option trade.

As traders we may have opinions about future market conditions, and we structure our trades accordingly. For example, you might expect that the market is going to move higher, or perhaps lower, so you look to open positions designed to benefit from the expected market move. The question we then struggle to answer is what our position will be worth if the market moves as we expect.

The "*Black-Scholes*" options pricing formula was the first modern pricing formula that could accurately calculate the price of an option. That formula has been improved upon, but we still generally refer to option pricing formulas as the Black-Scholes formula much like someone might ask for a "Kleenex" when they need a tissue.

The option pricing formulas use all of those several factors mentioned above to calculate the theoretical price of an option. So, we can factor in the anticipated market move and any changes we foresee in volatility, interest rates, and the like to project the likely price of any given options position we might care to open. But that is just the beginning...

We can also use the formula to quantify the relative effect each of the several factor has upon our options position. In effect, the option pricing formula quantifies the risk in a position through a series of variables that we collectively referred to as the “Greeks.”

We refer to these variables as the "Greeks" because each such variable has been assigned a Greek letter, or what sounds like a Greek letter, as a shorthand for identifying each element operating upon the value of an option contract. Mastering the option Greeks and understanding how they influence stock option pricing provides an insight into the risks that are inherent in an option position, and will allow you to better design and mange option trades.

## Delta - Directional Change

The first Greek variable that we will address is Delta, which is a measurement of the rate at which an option’s price will change given a one dollar increase (or decrease) in the underlying security’s price. For example, an option with a delta of .20 will increase .20 cents in value if the underlying stock increases by $1.00.

Delta serves other purposes for the options trader beyond measuring the sensitivity of a position to changes in the underlying security's price. It also provides us with a "hedge ratio" - measuring the equivalent number of shares of stock you may be long or short in the market. The "hedge ratio" tells us how many shares of stock we must buy or sell in order to eliminate directional risk.For example, if an option position has a delta of -100, it is the equivalent of being short 100 shares of stock. Purchasing 100 shares of stock would neutralize delta, reducing it to zero.

A third use for delta is as a measure of probability. Delta provides us with an approximate probability that an option will finish in-the-money as of its expiration. An option with a delta of .20 has a 20% chance of being in-the-money as of expiration. Conversely, that same option has an 80% probability of being out-of-the-money as of expiration.

To complicate matters further, an option's delta changes during the life of the option contract and will change, but we can also use the Greeks to anticipate how significant that change will be...

## Gamma - The Speed Of Change

As we mentioned, the delta of an option is not static. Delta changes with the change in the share price of the underlying stock. That change is measured by the "Gamma" of the option. Gamma references the anticipated change of the delta, for each incremental change in the price of the underlying stock.

## Theta - The Passage Of Time

Theta measures the amount of value that is lost from an option due to the passage of time. Options have limited life spans. They are what might be referred to as a "wasting asset." The rate at which value decays or is lost from the option is expressed as Theta.

Some option traders favor option selling strategies as this provides them with a positive theta. All else remaining constant, a short option position with a positive theta will gain value with each passing day while the option buyer's position will lose value from one day to the next.

## Vega - Volatility

Vega describes the sensitivity an options has to changes in implied volatility. Options tend to become more expensive in volatile markets. As the markets become more volatile, they also become more uncertain creating emotions of fear and greed in market participants. Those emotions may motivate a participant to pay more for a put option to protect his or her portfolio from a market drop.

A change in volatility can have profound consequences, positive and negative, upon an option position. In fact, the effects of volatility are as great - if not more so - than changes in the price of the underlying security. Vega provides us with insight into the effects we are likely to see as volatilty changes.

## Learn The Option Greeks Or Struggle

Developing an understanding of option pricing is necessary if you hope to trade options profitably. Whether you are trading simple long calls or puts, or perhaps selling covered calls, each of the factors discussed above can and will effect the valuation of the options you have bought and/or sold in your account.

Until you grasp the concepts embodied in these “Greeks”, you will struggle to understand why your trades act in seemingly erratic fashions and you will encounter increasing difficulty as you delve into more advanced options positions.

These concepts will begin taking on increasing importance as you start working with more advanced option strategies. Even simple “one legged” positions will respond to the differing forces of Delta, Vega and Theta. By adding or removing additional legs to a trade, you can exert control over how your position will respond to market changes.

As you begin adding additional legs, i.e., different option contracts to the position, the effect of those forces will be increased or decreased. As such, an astute options trader can quickly change how their trade will respond to further more market changes through carefully planned position adjustments.

Of course, if you do not understand how to manage the Greeks, you will face a very difficult time adjusting or repairing your option trades.

Our Options Foundations Course teaches the underlying principles that form the foundation of how options behave and respond to market changes. It provides a trader with the tools they need to select the "right" strategies, construct effective option positions, and manage them during changing market conditions.