Here are some potential topics for the research project. The background for all of these topics is Chapter 10 of the Miranda and Fackler textbook.
I can meet with you to discuss aspects of this work, either during scheduled class time or at other mutually convenient times. If you choose one of these topics, please let me know via email as soon as possible; first-come, first-served, one topic per student. If all topics are taken, I will cook up some more.
Section 11.1 presents several variations on a bond pricing model. We have zero-coupon bond pricing data on http://econ.bc.edu (Fama-Bliss discount bond prices and yields link) for a number of years and various tenors (terms to maturity). Use the bond pricing model (e.g. pp. 401-404) to construct estimates of bond prices for the various tenors and evaluate the accuracy of the model against the actual data (root mean squared error and mean absolute error criteria). Perform the experiment for different historical periods, perhaps based on the level of interest rates (see the Riskfree Rates data on that same econ.bc.edu page).
Sections 10.3.3, 10.3.7, 11.3.2 and 11.3.4 discuss the problem of renewable resource management. Use one of these models, with parameter values derived from some actual renewable resource, to illustrate the sensitivity of the optimal behavior to the model's parameters. Examples of renewable resources might be a fishery, rain forest timber, hunted game, etc. Present evidence that your model is calibrated to the specific details of the renewable resource you seek to model.
Sections 10.4 and 11.4 describe regime-switching models. For example, one might have two rate plans available from the cell phone company, one of which charges you per minute with no monthly fee, whereas the other gives you a certain number of 'free minutes' for a flat fee, with a lower per-minute charge over that amount. In reality, the provider has a menu of different 'regimes' based on number of free minutes, flat fee, and marginal cost for excess minutes. Use the regime-switching approach, with a continuous state variable representing the unknown number of hours your new boy(girl)friend will want to spend yakking with you per month, and realistic numbers for the rate plans chosen from some cell provider's site. Use more than two regimes if that is tractable.