If you'd like an introductory textbook approach on a level somewhat similar to Hamilton's, then "The Econometrics of Financial Markets" by John Y. Campbell, Andrew W. Lo, & A. Craig MacKinlay might be a choice, or, more precisely, the (rather short) section "Implementing Parametric Option Pricing Models" thereof:http://press.princeton.edu/TOCs/c5904.htmlFrom
the software point of view, R with the yuima package might be of use (go straight to the "Estimation of Financial Models" section of the slides):http://www.rinfinance.com/agenda/2011/StefanoIacus.pdf
Note, that when we say "estimation" (as in the above) we often mean statistical estimation (e.g. MLE) using the physically observed data, i.e., the parameter estimates you obtain are the ones corresponding to the physical measure P. Those might be useful e.g. for risk management.For (risk-neutral) pricing you need the risk-neutral parameters, i.e. the ones under the risk-neutral measure Q.You can make a transition if you know (or assume) something about the market price of risk or, equivalently, the stochastic discount factor (this is discussed in the aforementioned book).You can also calibrate directly under Q, minimizing some mispricing metric, but that's usually not "estimation" in the statistical sense.For instance, Trolle and Schwartz (2009) specify their model under the risk-neutral measure Q (in section "The model under the risk-neutral measure"), while the estimation is carried under the physical measure P ("Estimation procedure"). The link is the market price of risk, denoted with the upper-case Greek letter Lambda ("Market price of risk specification").