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3
votes
Using converted lognormal volatilities for negative rates in a lognormal Libor Market Model ...
I've not seen the abs function on the forward rate here before, the approximation comes from matching variances of a Black (Lognormal) and Bachelier (Normal) SDE. The Black SDE doesn't have this restr …
2
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Accepted
Can you shift a standard libor market model with regard to only at-the-money options?
The cash bond doesn't require a displacement, as such the denominator in your drift term should be $F_k(t)$ not $\bar{F}_k(t)$, i.e.
$dF_k(t) = \sigma_k(t)\bar{F}_k(t)\sum^k_{j=\beta(t)}\frac{\tau_j\r …