I recently saw a calculation where the expected 10-state-payoff-diagram of a stock with mean 6% and variance 20% was calculated through the risk neutral measure.
The method was as follow:
- Caluclation of physical quantile: i.e.LOGNORM.INV(prob=0.1;mean=0.06;var=0.2)
- risk-neutral probability of physical quantile: LOGNORM.VERT(phsyical quantile;0.00;0.20;cum)
- Discounted state price = Risk-Neutral Prob. of quant. 0.1 - RN Prob. of qant 0.0
- payoff in state 0.1 = investment in state / Discounted state price
Unfortunately, I cannot follow this procedure at all. First, it is based on historical values and second why use option theory on the possible payoffs of a stock? Is this a sensible approach in your opinion and do you have other examples where this is used?