You convert a state price vector into risk-neutral probabilities by multiplying each state price by the gross risk-free factor (1+i), where i is the per-period risk-free interest rate. This scaling transforms the monetary prices of Arrow-Debreu securities into a valid probability distribution that sums to 1.
Conditions: The state prices ψj are already determined.; i is the known per-period risk-free interest rate.; The market is a one-period finite-state model.
You convert a state price vector into risk-neutral probabilities by multiplying each state price by the gross risk-free factor (1+i), where i is the per-period risk-free interest rate. This scaling transforms the monetary prices of Arrow-Debreu securities into a valid probability distribution that sums to 1.
Conditions: The state prices ψj are already determined.; i is the known per-period risk-free interest rate.; The market is a one-period finite-state model.
The state price vector for this specific three-state market model is [24/55,4/55,2/5]. This vector is found by solving the linear system of pricing equations derived from the given asset payoffs and their common current price of 100.
Conditions: One-period securities market model.; Three possible scenarios (states).; Risk-free bank account with 10% interest (payoff 110 in all states).; Current price of each security is 100.; Security X payoffs: 220, 55, 0.; Security Y payoffs: 0, 0, 250.
The state price vector for this specific three-state market model is [24/55,4/55,2/5]. This vector is found by solving the linear system of pricing equations derived from the given asset payoffs and their common current price of 100.
Conditions: One-period securities market model.; Three possible scenarios (states).; Risk-free bank account with 10% interest (payoff 110 in all states).; Current price of each security is 100.; Security X payoffs: 220, 55, 0.; Security Y payoffs: 0, 0, 250.