First, you should realise that the spot price being £20 is irrelevant to the question. You don't need to calculate the individual prices of the options, and it is not possible to do so without making assumptions about the volatility of the underlying. $$ $$ Imagine a scenario where the spot price hits £30 at some point in the year. Then, with equal probabilities, the spot price will go up or down by the end of the year. Since there are no interest rates, this applies whether we treat the underlying stock as a Brownian motion, as a lognormal model or any similar process without drift. As a result, Option A will have a payoff of £1 twice as often as Option B, so Option A must be twice as valuable as Option B. $$ \text{Ratio} = \frac{C_A}{C_B} = 2 $$