The solution for the state price vector is unique because the coefficient matrix of the resulting linear pricing system has a nonzero determinant. A nonzero determinant guarantees that the system of linear equations has exactly one unique solution for the unknown state prices.
Conditions: The market model has three states and three traded assets.; The pricing system is a 3x3 linear system.; The coefficient matrix of the system is nonsingular (determinant is nonzero).
The solution for the state price vector is unique because the coefficient matrix of the resulting linear pricing system has a nonzero determinant. A nonzero determinant guarantees that the system of linear equations has exactly one unique solution for the unknown state prices.
Conditions: The market model has three states and three traded assets.; The pricing system is a 3x3 linear system.; The coefficient matrix of the system is nonsingular (determinant is nonzero).
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.