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Suppose we have a set of $N_T$ maturities $\tau_t$ and a set of $N_k$ strikes $K_k$ .For each maturity-strike combination $(\tau_t,K_k)$ we have a market price (for example) $Caplet(\tau_t,K_k)=C_{tk}$ and a corresponding model price $Caplet(\tau_t,K_k,\Lambda)=C^\Lambda_{tk}$ in which $\Lambda$ is Hull-Whit's Parameters. The first category minimize the ...


In practice, you can calibrate to either 1 month libor or 3 month libor, but not both. That's because there's a basis swap between 1 month libor and 3 month libor that can't be explained by your model.

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