Interesting question. Looking in my library, there is a short discussion of general Markov process bridgesin Sec. 2.VI.14 ('Tied Down Markov Processes') in Doob's 'Classical Potential Theory and Its Probabilistic Counterpart'. Ignoring the jumps, the generator for a general diffusion bridge is known; see for example (4.4) here (O. Papaspiliopoulos and G. Roberts)This shows that, at a minimum, you will need to start with an SV process with a known joint transition density. There actually aren't too many of those,but see my forthcoming book for the joint transition density for the Heston model and 3/2-model. If you want to add jumps,and keep a known (or at least tractable) joint transition density, one possibility is to use an independent stochastic time change. How to do the time change is also discussed in my book. (The book's table of contents may be found in this thread).How to do the time change *and* preserve your bridge conditioning information is *not* discussed in my book -- it's an interesting problem, left to you, since I don't know. Another approach to adding jumps is to try an affine jump-diffusion and see if you can construct the joint transition density.Whether either approach will be realistic enough for whatever your application is, is pretty hard to say in the abstract.I have found some decent results using the first (time-change) method for some joint SPX/VIX time series modeling. Anyway, those are some ideas on how to proceed or at least get started.
Last edited by Alan
on December 3rd, 2015, 11:00 pm, edited 1 time in total.