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The Greeks

# Overview

The Greeks are symbols that represent different risk attributes of options positions. They are used by traders to manage their portfolios by providing information on how positions will be affected by changes in the underlying product.

# Delta

Delta is the rate of change of the position price as a result of a change of the price of the underlying. If a position had a delta of 2, for every $1 increase in ETH price, the position would increase in value by approximately$2, and decrease by approximately $2 for every$1 decrease in the underlying. For negative delta positions (such as short ETH), the position increases in value when the underlying price decreases.

Gamma is the derivative of delta, with regards to the underlying price. This means that gamma is the rate of change of the position delta as a result of a change of the price of the underlying. If a position had a gamma of 0.01, for every $1 increase in ETH price, the position delta would increase in price by approximately 0.01. A position with positive gamma, such as long (ETH)² or GAMMA, means that as the price of the underlying increase, delta increases, meaning that the position value will increase at an faster rate. If the underlying price decreases, so does delta, meaning that the position value will decrease at a slower rate. # Vega Vega measures the change in a position price in relation to implied volatility. It represents the amount that a position price will increase or decrease for every 1% move in the implied volatility. Let's look an example position with a vega of 0.15, a price of$5, and the volatility of the underlying moves from 50% to 52%.
\begin{align*} \Delta Price=& \ Price \times \Delta Volatility \times Vega \\ =& \ 5 \times (52 - 50) \times 0.05 \\ =& \ 0.5 \\ \\ Price_{New} =& \ Price + \Delta Price \\ =& \ 5 + 0.5 \\ =& \ 5.5 \end{align*}
The ETH perpetual will have a vega of zero, meaning that it is not affected by volatility, where as (ETH)² will have a positive vega, meaning that the price of the position will increase as volatility increases.

# Theta

Theta is the measure of how a position price will change over time, provided that price and volatility do not change. For Predy perpetuals, theta represents the cost of funding each day. So for a long (ETH)² with a theta of -10, the position value will decrease by \$10 each day, assuming that price and volatility does not change.