What is a best-practice example on how to model callable bonds in a risk model - I focus on historical simulation (HS).
For plain-vanilla bonds the input factors for historical simulation could be
- the zero curve of the market (the currency)
- spread history
Then HS would model changes in interst rates of the currency (as systematic risk) and spreads either in issuer level (idiosyncratic) or rating level (rather systematic risk). Then we could reprice the bond in these scenarios.
Looking at callable bonds on the other hand we have to simulate/estimate the chance that the bond is called and when. To do this we could use an interest rate model which we would have to calibrate on future interest rate uncertainty. Then we can simulate the future and price the bond in these scenarios.
Market data that reflect this that I know are swaptions and captions. But these are instruments for the money market/capital market of a currency. However, the decisin of the issuer to call the bonds will depend on the interest rate level of the currency and the issuers spread.
How can we find a risk model that can be calibrated to readily available market data and that models the systematic as well as the idiosyncratic part of the call risk? How do industry solutions look like?