Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S9 / 3 / 2

Let $q$ be the risk-neutral up probability and $R=1.04$ the one-step risk-free gross return. Discounted asset price must be a martingale, soThe no-arbitrage condition $0.9<R<1.1$ is satisfied, so $q$ lies strictly between zero and one. This pricing probability need not equal the actual up frequency $p$.