Your question is not clear enough, neither is your proposed approach! callable bonds are usually priced by an IR pricing tree. It may also be possible to price the callable bond synthetically.

Missing terms --> interpolationMissing rating --> proxy or company's debtetc?

<r>How about Normal or shifted Lognormal? This could be useful for you: <URL url="http://www.wilmott.com/messageview.cfm?catid=4&threadid=98307"><LINK_TEXT text="http://www.wilmott.com/messageview.cfm? ... adid=98307">http://www.wilmott.com/messageview.cfm?catid=4&threadid=98307</LINK_TEXT><...

https://en.wikipedia.org/wiki/Short-rate_model

I was mixing up transition probabilities with survival probabilities; and hazard rate dynamics appear in both..

Thanks for this: "Numeraire_(T-1) x E[1_{tau>T} X_T / Numeraire(T)] + Numeraire_(T-1) x E[1_{tau<T} R/Numeraire(T)] "So we need to incorporate both 'survival' and 'default' states in pricing the instrument, which are two disjoint events.

<t>Let say you have to use a pricing tree for valuation of a defaultable callable (or putable) bond. Short interest rate is assumed to follow HW one-factor model. Hazard rate follows a similar HW one-factor model correlated with short rate. Recovery rate is constant. This framework is discussed in "...

<t>Hi Kelang,May I ask about the trick that speeds up pricing in your approach?Also, which measure is your pricing tree calibrated to? I assume it is calibrated to a forward measure. Now let say the tree is calibrated to risk-neutral measure, does anyone know any work-around to correctly price a cal...

Yes, as you said, liquid volatilities do not exist for xxcy swaptions. There may be a way to model this as an exchange option and use Margrabe formula. This would imply lognormality assumption for the two swap legs.

<t>Hi,Contingent CDS is a type of CDS, where the notional is the greater of zero and MtM value of the underlying derivative (usually some type of swap) at the time of default. This instrument is known as the prefect hedge for the counterparty CVA. Assuming there is no correlation between default of ...

<r>These reads could be useful:<URL url="http://wilmott.com/messageview.cfm?catid=8&threadid=75644andhttp://www.wilmott.com/messageview.cfm?catid=4&threadid=96809"><LINK_TEXT text="http://wilmott.com/messageview.cfm?cati ... adid=96809">http://wilmott.com/messageview.cfm?catid=8&threadid...

https://www.google.com/?gws_rd=ssl#q=va ... lio+matrix

<t>QuoteOriginally posted by: LH1984Thanks for you explanation Jhammer.One stupid question, what is the rational of having T here? It looks like the interpolation give higher weight on vol or variance with longer maturity.But the Vol is annualised vol, no? Is there any website/resource for this? Tha...

Thanks for your input, I will look into it

Here is the simple solution for linear interpolation of total vol in your example:$$ \sigma^{*^2} \times 2 = \frac{A^2 + 3B^2}{2} \quad \rightarrow \quad \sigma^{*} = \sqrt{\frac{A^2 + 3B^2}{4}}$$