April 19th, 2019, 12:18 pm
The ingredients of a good model for callable corporate bonds are yield curve dynamics, credit dynamics, and a model of call behavior as a function of the refinancing benefit. To start with the last one, you could use the classic textbook approach of setting the bond value equal to the minimum of the continuation value and the call price, but this will tend to overvalue the call option and assign the bond a bit too much duration. A better approach is to build in some refinancing costs or to borrow an empirical prepayment function from the mortgage world. You can model the credit dynamics via a stochastic hazard rate or by some asset value driven default process like Black & Cox or (more ambitiously) Duffie & Lando. Since most callable bonds are found in the HY space, the interest rate model choice is less important than what you assume about the credit behavior, so it would make sense to keep it fairly simple. Also, importantly, regardless of details of your credit and prepayment modeling choices, you will at best get a rough estimate of the value of the embedded call option, since you will be relying on several parameters that are impossible to estimate precisely. Ignoring the problem, e.g. by assuming a constant credit spread, will give you an imprecise estimate that is furthermore biased...