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Sensitivity Measures
There are six basic sensitivity measures associated with option pricing: delta, gamma, lambda, rho, theta, and vega -- the "greeks." The toolbox provides functions for calculating each sensitivity and for implied volatility.
Delta
Delta of a derivative security is the rate of change of its price relative to the price of the underlying asset. It is the first derivative of the curve that relates the price of the derivative to the price of the underlying security. When delta is large, the price of the derivative is sensitive to small changes in the price of the underlying security.
Gamma
Gamma of a derivative security is the rate of change of delta relative to the price of the underlying asset; i.e., the second derivative of the option price relative to the security price. When gamma is small, the change in delta is small. This sensitivity measure is important for deciding how much to adjust a hedge position.
Lambda
Lambda, also known as the elasticity of an option, represents the percentage change in the price of an option relative to a 1% change in the price of the underlying security.
Rho
Rho is the rate of change in option price relative to the risk-free interest rate.
Theta
Theta is the rate of change in the price of a derivative security relative to time. Theta is usually very small or negative since the value of an option tends to drop as it approaches maturity.
Vega
Vega is the rate of change in the price of a derivative security relative to the volatility of the underlying security. When vega is large the security is sensitive to small changes in volatility. For example, options traders often must decide whether to buy an option to hedge against vega or gamma. The hedge selected usually depends upon how frequently one rebalances a hedge position and also upon the variance of the price of the underlying asset (the volatility). If the variance is changing rapidly, balancing against vega is usually preferable.
Implied Volatility
The implied volatility of an option is the variance that makes a call option price equal to the market price. It helps determine a market estimate for the future volatility of a stock and provides the input volatility (when needed) to the other Black-Scholes functions.
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