Black-Scholes-Merton Model and the Greeks

The Black-Scholes-Merton model has six inputs (or five, if gamma is considered a sub-part of delta); five are known as the Greeks.

  1. Delta: The change in the option price per one dollar change in the underlying stock's price; alternatively, the change in the option price equals the change in the underlying multiplied by the option's delta.
  2. Gamma: The sensitivity of delta to the change in a price of the underlying asset.
  3. Theta: An option's price is affected by the amount of time to expiration; the longer the time, the more valuable the option. Theta is a measure of the rate of the time value decay of the option.
  4. Rho: This is an option's price sensitivity to a change in the risk free rate. Rho is commonly small and a European option's price is not heavily sensitive to a change in the interest rate.
  5. Vega: This is volatility sensitivity; specifically vega is option price sensitivity to the standard deviation of the asset's return. As volatility increases, options become more valuable.
  6. Strike (or Exercise) Price: This is the price at which the underlying asset can be bought (long call) or sold (long put) by the option holder. Excluding other factors, as strike prices go up calls are worth less and puts are worth more.

Summary of Input Impacts on Option Prices:

Interest RatesUpDown
Underlying Asset PriceUpDown
Time to ExpirationUpUp
Exercise/Strike PriceDownUp