What about this bet?

If in one year the temperature of London is equal or higher than today's, one gets paid £100, otherwise.

Suppose that there are no transaction costs, time value of money is 0%, participants are risk-neutral (they decide purely based on expected value) and temperature is a random walk process totally governed by constant annual volatility of 10%. This process implies that the temperature can go up and down in the future but in exactly one year's time it will most likely be where it is today.

How much should one pay today for this bet?