Never mind. I found  the answer.

Treasury Futures are often used to hedge interest rate risks. Given CtD, a Treasury Futures contract's DV01 is approximately       DV01 of Treasury Futures = DV01 of CtD x Conversion Factor and thus     Duration of Treasury Futures = Duration of CtD However, when I estimate the duration by the ratio...

Thank you both for your suggestions. The time to expiry is used only for the purpose of implied vol. As Pcaspers pointed out, as long as it meets the minimum requirements and makes sense, the actual convention does not matter too much. Thanks again.

Thanks for your reply. I have been trying many different ways, but that does not seem to be what is used in practice. For example, assume the curve date is 4/15/2019, the last publication date is 3/11/2019, the last fixing date is 2/1/2019, the option payment date is 4/17/2020 with corresponding fix...

An inflation cap/floor involves fixing date, publication date, payment date, etc. In order to calculate the implied volatility assuming either a Black or Normal model, what is the right way to calculate the expiry time, for example, in Bloomberg? Thanks!

Another questions is what to if the valuation date t is between observation date and publishing date, i.e. corresponding index observation date is in the past but it has not been published yet.

You should base it on the zv option exercise. There can be lots of intrinsic value to an option. Only the time value is eliminated when you turn off volatility.

Good point! Thanks

When calculating zvspread for a callable bond, should we use schedueld cash flows of the underlying bond or project cash flows based on estimated option exercise according to the zero volatility curve? In theory, option cost should 0 when the volatility is 0. Thanks.

An inflation price index is usually published with an observation lag of 2 or 3 months. Thus, payments are typically delayed by 2~3 months, which requires convexity adjustment. However, most documents on inflation modelling or textbooks do not consider this payment lag at all, but rather assume infl...

Cov(X,I{Y>K}) =E[X*I{Y>K}]-E[X]E[I{Y>K}] =(E[X|Y>K]-E[X])P(Y>K) The RHS does not seem meaningful in a general cocntext Cov(X,Y|Y=K)fY(K)=(E[X|Y=K]-E[X|Y=K])KdP(Y>K)/dK = 0? This does not seems correct either, since we know  Integal(Cov(X,Y|Y=K)f Y (K)dK) != 0 I am confused by the conditional covaria...

I am having difficulty figuring out whether Cov(X,I {Y>K} ) = Cov(X,Y|Y=K)f Y (K) holds in general or is only valid under certain circumstance. we know that in an integral form Cov(X,Y) = integral (Cov(X,I {Y>K} )dK) and Cov(X,Y) = Integal(Cov(X,Y|Y=K)f Y (K)dK) then, does  Cov(X,I {Y>K} ) = Cov(X,...

The problem was in skew calibration. Now everything seems fine, reasonably accurate with known bias. Gatarek, thank you very much for your help!

If I calibrate to only swaptions expiring in 25Y and 30Y, the calibration errors are still quite large. This implies that the swaption approximation formula does not work well for 25Y and 30Y swaptions.Mostly the model implied vols are more than 1% lower than market vols.

Bootstrap is OK.

Yes,but I have some problem with 20y and 30y. For some reason, resultant Libor vols for those two expirations are biased torward 0 and quite volatile along swap maturity as well. There must be something going on.

If you want a linear formula for volatility, you must take  https://www.risk.net/derivatives/interest-rate-derivatives/1500291/fully-lognormal-libor-market-model This not so tough to implement although looks horrible. You may go nonlinear as in the original paper but it doesn't give much improvemen...