Option risk management

Option sensitivities and risks
Option sensitivities (also known as the ‘greeks’) describe how option values change
when the variables and parameters change. We looked at this subject in discussing
the variables that go into the Black–Scholes model. Now, we will discuss their
application to option risk management.
We will begin by defining the key sensitivities, and then describe how they are
employed in option risk management practice:
Ω Delta is the sensitivity of option value to changes in the underlying asset price.
Ω Gamma is the sensitivity of the option delta to changes in the underlying asset
price.
Ω Vega is the sensitivity of the option delta to changes in the implied volatility of
the underlying asset price.
Ω Theta is the sensitivity of the option delta to the declining maturity of the option
as time passes.
Formally, all the option sensitivities can be described as mathematical partial
derivatives with respect to the factors that determine option values. Thus, delta is
the first derivative of the option’s market price or fair value with respect to the price
of the underlying, gamma is the second derivative with respect to the underlying
price, vega is the derivative with respect to implied volatility, etc. The sensitivities are defined as partial derivatives, so each one assumes that the other factors are
held constant.