Exponential Splines
Subtype of MethodCorresponds to the ExponentialSplinesFitting method in QuantLib.
The resulting discount factor P(T) for maturity T depends on whether a constrain at 0 is imposed or not.
Without the constrain, it depends on 10 parameters and has the form:
P(T) = α₁e⁻ᵏᵗ + α₂e⁻²ᵏᵗ + ... + α₉e⁻⁹ᵏᵗ
with parameter ordering: α₁, α₂, ..., α₉, κ
With the constrain, it depends on 9 parameters and has the form:
P(T) = βe⁻ᵏᵗ + α₁e⁻²ᵏᵗ + α₂e⁻³ᵏᵗ + ... + α₈e⁻⁹ᵏᵗ
where β = 1 - α₁ - α₂ - ... - α₈
and parameter ordering: α₁, α₂, ..., α₈, κ
See: Li, B., E. DeWetering, G. Lucas, R. Brenner and A. Shapiro (2001): "Merrill Lynch Exponential Spline Model." Merrill Lynch Working Paper
Warning: Convergence may be slow.