BitCoin Price Index -Studies on Relation to Network Hashrate and Block Difficulty?
I know of one researcher off hand who has worked in this area, Adam Hayes. You can find his papers on the subject at:


http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2648366
http://www.economicpolicyresearch.org/econ/2015/NSSR_WP_052015.pdf


You could also look around on http://arxiv.org/. Just searching for 'bitcoin price', I found:


http://arxiv.org/pdf/1406.0268.pdf
http://arxiv.org/pdf/1405.4498.pdf