114 Frequently Asked Questions In Quantitative Finance
This is useful for seeing how your hedge position will
change with time, for example up until the next time you
expect to hedge. This can be important near expiration.Colour The colour is the rate of change of gamma with
time.
∂^3 V
∂S^2 ∂t.Vanna The Vanna is the sensitivity of delta to volatility.∂^2 V
∂S∂σ.This is used when testing sensitivity of hedge ratio to
volatility. It can be misleading at places where gamma
is small.Vomma or Volga The Vomma or Volga is the second
derivative of the option value with respect to volatility.∂^2 V
∂σ^2.Because ofJensen’s Inequality, if volatility is stochastic
the Vomma/Volga measures convexity due to random
volatility and so gives you an idea of how much to add
(or subtract) from an option’s value.Shadow greeks The above greeks are defined in terms
of partial derivatives with respect to underlying, time,
volatility, etc.while holding the other variables/para-
meters fixed. That is the definition of a partial deriva-
tive.^3 But, of course, the variables/parameters might, in
practice, move together. For example, a fall in the stock(^3) Here derivative has its mathematical meaning of that which is
differentiated not its financial meaning as an option.