The option Greeks are a measure of different dimension to the risk in an option position. The Option Greeks measure the sensitivity of the price of stock options in relation to 4 different factors; Changes in the underlying stock price, interest rate, volatility, time decay. The aim of traders is to manage the Greeks in order to manage their overall portfolio.

There are five option Greeks namely Delta, Gamma, Theta, Vega & Rho. Option Greeks allow option traders to objectively calculate changes in the value of the option contracts in their portfolio with changes in the factors that affects the value of stock options. The ability to mathematically calculate these changes gives option traders the ability to hedge their portfolio or to construct positions with specific risk/reward profiles. This alone makes knowing the Option Greeks priceless in options trading.

The option's delta is the rate of change of the price of the option with respect to its underlying security's price. The delta of an option ranges in value from 0 to 1 for calls and 0 to -1 for puts and reflects the increase or decrease in the price of the option in response to a 1 point movement of the underlying asset price. Far out-of-the-money options have delta values close to 0 while deep in-the-money options have deltas that are close to 1.

As the delta can change even with very tiny movements of the underlying stock price, it may be more practical to know the up delta and down delta values. For instance, the price of a call option with delta of 0.5 may increase by 0.6 point on a 1 point increase in the underlying stock price but decrease by only 0.4 point when the underlying stock price goes down by 1 point. In this case, the up delta is 0.6 and the down delta is 0.4.

Passage of time and its effects on the delta

As the time remaining to expiration grows shorter, the time value of the option evaporates and correspondingly, the delta of in-the-money options increases while the delta of out-of-the-money options decreases.

Changes in volatility and its effect on the delta

As volatility rises, the time value of the option goes up and this causes the delta of out-of-the-money options to increase and the delta of in-the-money options to decrease.

Delta Neutral Hedging is an option trading technique used to protect a position from short term price swings. It is the construction of positions that do not react to small changes in the price of the underlying stock. No matter if the underlying stock goes up or down, the position maintains its value and neither increases nor decreases in price. In option trading, this is also known as Delta Neutral Hedging. This is particularly useful for long term stocks, buy and hold strategy. The advantage of using delta neutral hedging is that it not only protects your position from small price changes during times of uncertainty such as near resistance or support levels, but it also enables your position to continue to profit from that point onwards if the stock rises or falls strongly.

A share has a delta value of 1 as its value rises by Rs.1 for every Rs.1 rise in the stock. If one owns 100 shares of a stock, you can attain a delta neutral position by buying 2 contracts of it's at the money put options with delta value of -50 per contract. 100 (delta value of 100 shares) - 100 (2 x 50) = 0 Delta.

Any small drop in the price of the shares will be instantly offset by a rise in the value of the put options. Any small rise in the price of the shares will also be offset by a drop in the value of the put options. This is an extremely popular option trading technique used by option traders who owns shares to protect the value of that position when the stock reaches a strong resistance level.

This is particularly useful for long term stocks, buy and hold strategy. The advantage of using delta neutral hedging is that it not only protects your position from small price changes during times of uncertainty such as near resistance or support levels, but it also enables your position to continue to profit from that point onwards if the stock rises or falls strongly.

The option's gamma is a measure of the rate of change of its delta. The gamma of an option is expressed as a percentage and reflects the change in the delta in response to a one point movement of the underlying stock price. Like the delta, the gamma is constantly changing, even with tiny movements of the underlying stock price. It generally is at its peak value when the stock price is near the strike price of the option and decreases as the option goes deeper into or out of the money. Options that are very deeply into or out of the money have gamma values close to 0.

Suppose for a stock XYZ, currently trading at 47, there is a JAN 50 call option selling for Rs.2 and let's assume it has a delta of 0.4 and a gamma of 0.1 or 10 percent. If the stock price moves up by Rs.1 to Rs.48, then the delta will be adjusted upwards by 10 percent from 0.4 to 0.5. However, if the stock trades downwards by Rs.1 to Rs.46, then the delta will decrease by 10 percent to 0.3.

As the time to expiration draws nearer, the gamma of at-the-money options increases while the gamma of in-the-money and out-of-the-money options decreases. Changes in volatility and its effects on the gamma When volatility is low, the gamma of at-the-money options is high while the gamma for deeply into or out-of-the-money options approaches 0. This phenomenon arises because when volatility is low, the time value of such options are low but it goes up dramatically as the underlying stock price approaches the strike price. When volatility is high, gamma tends to be stable across all strike prices. This is due to the fact that when volatility is high, the time value of deeply in/out-of-the-money options is already quite substantial. Thus, the increase in the time value of these options as they go nearer the money will be less dramatic and hence the low and stable gamma.

The option's theta is a measurement of the option's time decay. The theta measures the rate at which options lose their value, specifically the time value, as the expiration date draws nearer. Generally expressed as a negative number, the theta of an option reflects the amount by which the option's value will decrease every day.

A call option with a current price of Rs.2 and a theta of -0.05 will experience a drop in price of Rs.0.05 per day. So in two days' time, the price of the option should fall to Rs.1.90.

Passage of time and its effects on the theta

Longer term options have theta of almost 0 as they do not lose value on a daily basis. Theta is higher for shorter term options, especially at-the-money options. This is pretty obvious as such options have the highest time value and thus have more premiums to lose each day. Conversely, theta goes up dramatically as options near expiration as time decay is at its greatest during that period.

Changes in volatility and its effects on the theta

In general, options of high volatility stocks have higher theta than low volatility stocks. This is because the time value premiums on these options are higher and so they have more to lose per day.

The option's Vega is a measure of the impact of changes in the underlying volatility on the option price. Specifically, the Vega of an option expresses the change in the price of the option for every 1% change in underlying volatility. Options tend to be more expensive when volatility is higher. Thus, whenever volatility goes up, the price of the option goes up and when volatility drops, the price of the option will also fall. Therefore, when calculating the new option price due to volatility changes, we add the Vega when volatility goes up but subtract it when the volatility falls.

A stock XYZ is trading at Rs.46 in May and a JAN 50 call is selling for Rs.2. Let's assume that the Vega of the option is 0.15 and that the underlying volatility is 25%.If the underlying volatility increased by 1% to 26%, then the price of the option should rise to Rs.2 + Rs.0.15 = Rs.2.15.

However, if the volatility had gone down by 2% to 23% instead, then the option price should drop to Rs.2 - (2 x 0.15) = Rs.1.70

Passage of time and its effects on the Vega

The more time remaining to option expiration, the higher is the Vega. This makes sense as time value makes up a larger proportion of the premium for longer term options and it is the time value that is sensitive to changes in volatility.

Rho is the change in option value that results from movements in interest rates. The value is represented as the change in theoretical price of the option for a 1 percentage point movement in the underlying interest rate. For example, say you're pricing a call option with a theoretical value of 2.50 that is showing a Rho value of .25. If interest rates increase from 5% to 6%, then the price of the call option, theoretically at least will increase from 2.50 to 2.75.Unlike the other Option Greeks, Rho is larger for options that are in the money and decreases steadily as the option moves out of the money.

Option Rho also increases with a greater amount of time to expiration. These two factors are explained by the effect that interest rates have on the cost of carry of an option. ITM options, and options that have more time until expiration, will have higher premiums and therefore require more cash to hold the option until the expiration date. Rho is generally the least important of all the Option Greeks. This is because option traders tend to focus on trading options that are close to expiration and out of the money.