I have a stock with mu 6% and sigma 20% following a random walk and I would like to to calculate the Conditional expected Value of the stock in 10 states with equal probability (10%). Meaning, I would like to know how much the stock pays in the deciles from worst case to best case.
Would it be correct, to first calculate the physical quantiles of the distribution and afterwards the risk-neutral probabilities of the physical quantiles?
In the end I would like to say that:
Given a stock with these characteristics your expected payoff in a 10 state-digram would look like this: (with the returns values of course made up right now)
Probability Return 10% -30% 10% -25% 10% -10% 10% -5% 10% 15% 10% 20% 10% 30% 10% 40% 10% 50% 10% 70%