I'm analyzing the data from a large peer-to-peer lending platform. More precisely, I am analyzing the relationship between the interest rates that are charged by lenders and the loan amount that they grant. I make a distinction between high-risk (bad credit rating) and low-risk (good credit rating) borrowers.
I am doubting whether I should assume a linear relationship between interest and amount (for both high-risk borrowers and low-risk borrowers) or a quadratic relationship. See the pictures below, these are the relationships I find.
Now does this make sense? The most basic assumption would be that lenders would charge higher interest rates to high-risk borrowers as the probability of default will significantly increase when the granted loan amount increases (i.e. a positive linear relationship between interest and granted loan amount), but this is not the case according to the data. In fact, lenders seem to charge less interest as high-risk borrowers are given larger loans.
What could be a possible explanation for this? My guess is that for high-risk borrowers, lenders seem to compete with other lenders by lowering interest rates as the loan amount increases, as they already charging them (HR borrowers) high amounts of interest. However, at a certain point (around €7,000) they start to charge more interest again, either because (1) the amount of competition decreases and lenders gain more individual bargaining power or (2) the amount of risk that a higher loan bears at this point is so big that lenders want to be compensated by charging more interest.
All in all, I find it kinda difficult to interpret these results. Are there any people here that could offer better explanations?