Deep Gamma
Key Deep Gamma in Curve Booster refers to a boolean flag that is relevant only when Use Gamma is TRUE
When TRUE, the second order derivatives ∂²xᵢ/∂rⱼrᵤ of the internal quantities on the peg nodes relative to all relevant market quotes are considered.
The latter include market quotes that are not a direct input to the curve under construction, but nevertheless affect its construction because they are input to one or more of the required exogenous curves.
The typical example is the construction of a Libor curve that uses market quotes of deposits, futures and swaps as direct input and also takes an exogenous OIS curve for discounting purposes.
Then the ρ market quotes r₁, r₂, ..., rᵨ in the Jacobi matrix of the first order derivatives ∂xᵢ/∂rⱼ encompass the deposit, futures and swap rates, but also the OIS market rates that are used to build the exogenous OIS curve.
Under the TRUE setting, all second order derivatives ∂²xᵢ/∂rⱼrᵤ are considered, even those where eitherthe rⱼ or the rᵤ, or even both, are OIS rates, even though the OIS rates have only an indirect inpact on the libor curve.
Under the FALSE setting, only those second order derivatives ∂²xᵢ/∂rⱼrᵤ are considered where both their rⱼ andrᵤ are direct inputs in the curve being constructed.
In the above example, a FALSE setting would mean that only the second order derivatives wrt deposit, futures and swaps are considered.
The TRUE setting has the drawback that it is more time consuming during the initial phase when the derivatives are constructed.
It has though the advantage that this construction needs to occur less frequently as the market quotes keep changing because the implied curve internal quantities are closer to the true values.
It is not clear whether the TRUE setting is necessary to reach good convergence.
It may be the case that a curve construction based on a FALSE setting delivers satisfactory results in a more efficient manner.