# Impact analysis of parameters in the 2 Factor Hull White Model

Through the 2-Factor-Hull White Model you can model the yield curve if you have the parameters $a, b, \sigma, \eta$ given. Is there any way to measure the impact of these parameters on the yield curve (without calibration the model), like the the sensitivity analysis (Greeks).

\begin{align} \begin{split} r(t) & = x(s) e^{-a(t-s)} + y(s) e^{-b(t-s)} + \sigma \int_s^t e^{-a(t-u)} dW_1(u) \\ &+ \eta \int_s^t e^{-b(t-u)} dW_2(u) + \varphi(t) \label{eq:3.16} \end{split} \end{align}

where the bond price is given by

\begin{align} P(t,T) & = \frac{P(0,T)}{P(0,t)} e^{-\frac{1- e^{-a(T-t)}}{a} x(t) - \frac{1-e^{-b(T-t)}}{b} y(t) - \frac{1}{2} (V(0,T) - V(t,T) - V(0,t))} \end{align} with

$x(t) = x(s) e^{-a(t-s)} + \sigma \int_s^t e^{-a(t-u)} dW_1(u)$

$y(t) = y(s) e^{-b(t-s)} + \eta \int_s^t e^{-b(t-u)} dW_2(u)$

The dynamics are given by :

$dx(t) = -a x(t) dt + \sigma dW_1(t), x(0) = 0 \\ dy(t) = -by(t) dt + \eta dW_2(t), y(0) = 0$
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