### Option Greeks (Delta, Theta, Gamma, Vega, Rho)

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We are pleased to announce that now you can view greeks of options traded at NSE. If you trade options, then its important to understand what is the risk in your positions. Each greek letter measures a different dimension of risk in an option position. For an introduction to options, we suggest reading investopedia. Greek letters are calculated using black scholes model.

You can find greek letters of options in "Futures & Options" section on every stock page. We will talk about greeks with the help of an example. RELIANCE call option with strike price Rs.860 closed at Rs.6.75, while underlying RELIANCE stock closed at Rs.843. Reliance Call (Rs860 Strike Price) greeks are:

• Delta: 0.35
• Theta: -1.85
• Gamma: 0.0092
• Vega: 40.1
• Rho: 4.71

Now we discuss each greek letter in detail:

#### Delta

The delta of an option is defined as the rate of change of option price with respect to the price of underlying equity/asset. As example, delta of reliance call option (Rs.860 Strike) is 0.35 which means if the stock price goes up by Rs.10 then option price will tend to go up by Rs.3.5. If you have one lot (250 options) of thse reliance options, then delta of your position is 250x0.35 = 87.5.

You can use delta to do hedging which is also called as delta-hedging. Suppose you have sold one lot of above mentioned reliance options. Then delta of your position is -87.5. Now you lose money if stock goes up. Delta of a stock is 1. So if you buy 87.5 (~88) stocks of reliance. Then delta of your overall position becomes zero and position is delta neutral. Now your option position is hedged.

It is important to relaize that as delta changes, your position remains delta hedged for only a relatively short period of time. The hedge has to be adjusted periodically. This is known as rebalancing. This is also known as dynamic hedging. If you don't rebalance then its called as static hedging or hedge-and-forget.

Delta decreases as strike price of option increases and it increases with increasing time to expiry. Delta of a long call option is positive and delta of a long put option is negative.

#### Theta

The theta of an option is the rate of change of value of option with respect to passage of time with all else remaining same. It is also referred as the time decay of an option. In the example above, theta is -1.85 which means that with each trading day, value of the option decreases by Rs1.85 if all else remained same.

Theta is usually negative for an option. This is because, as time passes with all else remaining the same, the option tends to become less valuable.

#### Gamma

The gamma of an option is the rate of change of option delta with respect to the price of the underlying asset. It is the second partial derivative of option price with respect to asset price.

When you are doing dynamic hedging then rebalancing to keep the portfolio delta neutral need to be made infrequently.

In the example above, gamma is 0.0092 which means when stock price changes by Rs.1 then delta of option changes by 0.0092.

#### Vega

The vega of an option is defined as the rate of change of value of option with respect to volatility of underlying asset.

In the example above, vega is 40.1 which means a 1% increase in volatility of reliance stock price will result in 0.01x40.1= Rs.0.4 increase in option price and vice-versa.

If you wish to make your porfolio to be not dependent on volatility then you make it vega neutral by taking appropriate option positions.

#### Rho

The rho of an option is defined as the rate of change of value of option with respect to the interest rate.

In the example above, vega is 4.71 which means a 1% increase in interest rate will result in 0.01x4.71= Rs.0.04 increase in option price and vice-versa.

Rho of a long call option is positive and rho of long put option is negative.

#### Caveats

In practice, if you are doing delta hedging, rebalancing should be done depending on gamma of your portfolio. While rebalancing, transaction costs should be considered beforehand.

Happy Investing!

Clearnifty Team.