110 Frequently Asked Questions In Quantitative Finance
What are the Greeks?
Short Answer
The ‘greeks’ are the sensitivities of derivatives prices
to underlyings, variables and parameters. They can be
calculated by differentiating option values with respect
to variables and/or parameters, either analytically, if
you have a closed-form formula, or numerically.Example
Delta,=∂∂VS, is sensitivity of option price to the stock
price. Gamma,=∂(^2) V
∂S^2 , is the second derivative of the
option price to the underlying stock, it is the sensitivity
of the delta to the stock price. These two examples are
called greek because they are members of the Greek
alphabet. Some sensitivities, such as vega=∂∂σV,are
still called ‘greek’ even though they aren’t in the Greek
alphabet.
Long Answer
Delta The delta,, of an option or a portfolio of options
is the sensitivity of the option or portfolio to the under-
lying. It is the rate of change of value with respect to
the asset:
=
∂V
∂S
.
Speculators take a view on the direction of some quan-
tity such as the asset price and implement a strategy to
take advantage of their view. If they own options then
their exposure to the underlying is, to a first approxima-
tion, the same as if they own delta of the underlying.
Those who are not speculating on direction of the
underlying will hedge by buying or selling the under-