Greeks Based on Black-Scholes
Option Pricing Model
the sensitivity of the option from its
parameters. In this section, we will explore each of the Greeks
will begin with Delta.
Theta refers to the rate of time
decay for an option. It is the first differential of the option
value with respect to time. Holding all other things constant, an
option loses value as it approaching to the expiration day. Theta
measures the cost of holding an option long, and the reward fo writing
Vega measures the relationship between the volatility of the underlying asset and the option value. It is the first differential of the option price with respect to the volatility (standard deviation). The more volatility the underlying asset is, the more valuable the option becomes since the chance for the option to be deep-in-the-money is greater.
input and output are shown as followed. Note that the sign for
each of the greeks indicates the direction that the option price will
go when the corresponding parameter changes.