currently I am working on a problem regarding state contingent claims.
I have 5 securities (one of the security is a risk-free security) and in the next period, these securities will end up in one of 4 possible states (where the cashflows differ in each state for each security).
I have the following information available:
- Current Prices of the securites
- Cashflows of the securities for the next period
I already managed to calculate the risk-free probability measures for each state and the state prices.
Now my question is, how to get the physical prob. measure for each state?
My Idea was the following:
the risk free prob. measure can be calculated with the formula:
- Prob(RF)= [m(s)/E(m)]*Prob(physical)
rerange the formula for prob(physical) gives:
- Prob(Physical)= [Prob(RF)*E(m)]/m(s)
- Prob(RF) = Risk free prob. measure
- Prob(physical) = Physical prob. measure
- E(m)= Sum of all state prices
- m(s)= Discount Factor
but here my problem is, that I dont know the discount factor for each state. Unfortunately, all books I´ve looked into, define the discount factor by first derivatives of utility functions. I dont have any utility functions available, so that wasnt a great help, and the reason why I´m struggling with that.
I would be very happy about an idea how to get to m(s) or another approach to get the physical prob measure.
I hope someone can give me some hints.