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.
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 bank account contributes 110 in every state because it is a risk-free asset that pays 10% interest per year. Investing 100 today guarantees a return of 110 at time one, regardless of which of the three possible scenarios occurs.
Conditions: The bank account is risk-free.; The bank account pays 10% interest per year.; The initial investment (current price) is 100.; The model is a one-period setting with multiple states.
The bank account contributes 110 in every state because it is a risk-free asset that pays 10% interest per year. Investing 100 today guarantees a return of 110 at time one, regardless of which of the three possible scenarios occurs.
Conditions: The bank account is risk-free.; The bank account pays 10% interest per year.; The initial investment (current price) is 100.; The model is a one-period setting with multiple states.
The state prices ψj represent the prices of Arrow-Debreu securities, which are monetary values and do not necessarily sum to 1. The transformed vector qj represents risk-neutral probabilities, obtained by multiplying each state price by the gross risk-free factor (1+i).
Conditions: The market is a one-period finite-state model.; ψj are the solved state prices (Arrow-Debreu security prices).; i is the per-period risk-free interest rate.; qj is defined as qj=(1+i)ψj.
The state prices ψj represent the prices of Arrow-Debreu securities, which are monetary values and do not necessarily sum to 1. The transformed vector qj represents risk-neutral probabilities, obtained by multiplying each state price by the gross risk-free factor (1+i).
Conditions: The market is a one-period finite-state model.; ψj are the solved state prices (Arrow-Debreu security prices).; i is the per-period risk-free interest rate.; qj is defined as qj=(1+i)ψj.