## What are Greeks?

Traders in derivatives must be aware of the dangers they are taking. The Greek letters (or Greeks, frequently referred to) are meant to educate people about these dangers. Some Greek letters deal with price changes in the underlying asset; others deal with volatility changes, yet others deal with interest rates and dividend yields.

Typically, a trader is limited to how large the Greek letters can be. Suppose one of the Greek letters exceeds the applicable limit near the end of the trading day. A trader must either execute a trade that corrects the situation or seek special permission from the risk management function to maintain the existing position.

## Examples of Greek:

The most common Greeks include the **Delta, Gamma, Theta,** and **Vega,** the first partial derivatives of the options pricing model.

- Delta: It is a ratio between the change in the price of an options contract and the corresponding movement of the underlying asset’s value. For example, if a stock option for XYZ shares has a delta of 0.45, if the underlying stock increases in market price by \$1 per share, the option value will rise by \$0.45 per share, all else being equivalent.
- Gamma: Gamma is commonly calculated as a change in the delta for every one-point change in the underlying price. A 220 call, for example, has a delta of 30 and a gamma of 2 if the futures price is 200. The difference is now 32 if the futures price rises to 201.
- Vega: Vega is the Greek letter that measures the trader’s exposure to volatility. It represents the amount that an option contract’s price changes in reaction to a 1% change in the underlying asset’s implied volatility.

vega=∂ f/∂ σ - Theta: Theta can be thought of as the rate of decline in the value of an option as time passes.

$ \theta = \frac{\delta V}{\delta\tau} $

Where:

∂ – the first derivative

V – the option’s price (theoretical value)

τ – the option’s time to maturity

## Why are Greeks important?

The Greeks are essential risk management tools. Each Greek calculates the sensitivity of a portfolio’s value to a tiny change in an underlying parameter, allowing component risks to be managed separately and the portfolio rebalanced to reach the desired exposure; see, for example, delta hedging.