I was given this question on interview and couldn't find an answer in time (it is a software developer job in a place that deals with options). Can someone explain how to do this or point me to a good source of material?
Given two European options - a call $C$ and a put $P$ - struck at $K$, expiring at time $T$, on an underlying asset priced at $S_t$ today, derive the formula for the implied asset financing rate, i.e., the asset borrow/loan or repo rate. Assume the discount rate is $r$ and the dividend yield on the asset is $q$, both annual continuously compounded.
My answer was: Interest rate = [(future value/present value) – 1] x year/number of days, that's what I was able to find online at the time.