I just read a working paper and I am trying to get behind the authors' logic of their calculation of a ten-state payoff-diagram of a specific stock (ten payoff states with equal probability).
In their paper they simulate a year worth of daily stock returns with with mu = 0.06 and sigma = 0.2.
To calculate the diagram they first calculate the physical quantiles of the lognormal distribution.
d1 = qlnorm(0.1, 0.06, 0.2), ..., d10 = qlnorm(1, 0.06, 0.2)
Then they assume a risk-free rate of 0% and calculate the risk-neutral probability of the physical quantile
p1 = plnorm(d1, 0.00, 0.2), ... , p10 = plnorm(d10, 0.00, 0.2)
Finally the 10-state payoff digram looks like this
s1 = 1/p1 - 1, s2 = 1/(p2-p1) -1, ... , s10 = 1/(p10-p9) -1
Could someone explain the logic behind this or link me to an article where it explained?