Define the following tools with respect to option derivatives: (a) Delta (b) Gamma (c) Theta (d) Vega.

Delta: An options delta is used to measure the anticipated percentage of change in the premium in relation to a change in the price of the underlying security. Gamma: Gamma measures the expected change in the delta factor of an option when the value of the price of the underlying security rises. Theta: The theta derivative attempts to measure the erosion of an option's premium caused by the passage of time. It is designed to predict the daily rate of erosion of the premium. Vega: Vega is concerned with the volatility factor of the underlying stock. Vega measures the amount by which the premium will rise when the volatility factor of the stock increase.