Hi all,when calibrating a structural pricing model, I assume stochastic processes under the risk-neutral measure for the state variables (short rate, firm's assets, etc.). Then I calculate prices as present-discounted cashflows, which is possible because the processes are under the risk-neutral measure. And then I observe prices and other quantities and estimate the unknown parameters.So my question is this: Is there not a problem with this approach, since how real probabilities transform into risk-neutral ones depends on required returns (= risk premia = discount rates) in the markets, which are not constant over time?Or is this one of the basic assumptions (instead of a problem) we make when using structural models?Any thoughts by more experienced people who see through these things are appreciated!Thanks a lot.

Bonds are not my area, but I think your question can be addressed using equity language.Assuming a time-homogeneous parameterized risk-neutral model is not, in itself, a logical contradiction ofa world with time-varying risk premia. For example, I suppose Black and Scholes could have said: let's suppose a stock price follows (*) [$] dS = (r + \alpha_t) S dt + \sigma S dW_t [$], where [$]\alpha_t[$] is a time-varying risk premia.Now, we will show that options on S have a unique price independent of [$]\alpha_t[$], as if the stock price evolved as(**) [$] dS = r S dt + \sigma S dW^*_t [$]. However, the logical contradiction with (*) arises when successive point-in-time calibrations of theoption formula derived from (**) show that theremaining parameters, putative constants -- esp [$]\sigma[$] -- vary widely in time (and by strike). This latter time-contradictioncan be reduced by adopting an econometric attitude toward your model. That is, *final* model being tested,say for a derivative price [$]C_t[$] (a bond in your case) is that(***) [$] C_t = C_t^{RN model} + \epsilon_t[$], and this is meant to hold over time, not just cross-sectionally.Of course, the fit of (***) may or may not be any good in a particular case.Ideally, you should try to parameterize your risk premia and fit the statistical process to the returnsobserved in your data also. In other words, calibrations should ideally be a joint calibration ofboth a risk-neutral and statistical process and should be done with a long time-series of (cross-sectional) data. For example, sticking with (*) and (**), the risk premia on the derivatives, say call prices, should be(from pg 15 of my book),[$] \alpha^{(C)}_t - r = \Omega(S_t,t) (\alpha_t - r) [$], where [$] \Omega(S,t) = \frac{S C_S}{C}[$]This could be parameterized and promoted to an econometric model with an error term again.For bonds, of course, there is a huge literature about risk premia.So, the art of good risk-neutral modelling is being aware of the related statistical (return premia) modelling that has alreadybeen done. This may well lead you to incorporating some non-stationary behavior into your risk-neutral model.Not because of a logical contradiction, but to improve the model.