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Monte Carlo simulation for pricing a zero coupon bond To assess the value $V_t$ of a zero coupon bond $B_{T, t}$ issued today at time $t$ with expiry at time $T$, you can do so using the formula $$V_t = \mathbb{E}\left(\exp\left(-\int_t^T r_s \mathrm{d}s\right)\underbrace{B_{T, T}}_{=1}\right).$$ Now if you're using the CIR model the nice thing is that the ...
For the long term mean "b", do we use effective Fed Fund rates? or 3m T-bills? I don't think so. For this particular short rate model, you have to provide 3 input parameters, namely: $a$, $b$ and $\sigma$ (using your notation). I believe that $a$ and $b$ are obtained by fitting the current term structure of zero coupon bonds $P^M(0,T)$ present in ...