lb trading

ntarsis is in an HRT interview. the interviewer begins describing the problem:

“you observe an underlying index price continuously. a contract pays $1 if the price at the end of a fixed time window (e.g., 15 minutes) is at least the price at the start. what’s the contract’s fair YES probability?”

help ntarsis pass the interview by creating a function that maps changes in the underlying price (and time remaining) into shifts in the contract’s fair YES probability.

ntarsis begins explaining his solution. the interviewer follows up:

“what if, instead of the exact start/end price, the contract uses 60-second rolling averages at the start and end of the window?”