hello allConsider a binary option with the following payoff: +1, when 30y-10y swap rate > 0 0 , elseToday is time=0, the spread is observed at time t and the payoffis paid at time T.I am trying to price and/or extract the probability that 30y-10y>0, under the assumption that the spread is distributed under Normal(mu,sigma),where mu is the mean of the distribution of spreads and sigma = sqrt(251)*[ daily changes in 30y-10y spreadsWould someone be so kind to provide the Normal diffusion process, the expression describing the distribution of the of the Spreadat time t under the Normal model, the probability that the spread >0.Is this correct?I would greatly appreciate your help.

Unless I misunderstand you, the problem is trivial. At time t the expected spread is S(0) + mu*t and the standard deviation is sigma*t^0.5, where S(0) is the spread at time zero. All you need is the probability that a standard Normal variate is greater than [S(0) + mu*t]/(sigma*t^0.5). You can look it up in a table, or use the Excel funtion NORMDIST(0,S(0) + mu*t,sigma*t^0.5,TRUE).