المدربGiven the real-world probabilities of the states, the state-price density is ; every price is an expectation under : . It is the ratio of the risk-neutral to the real-world probability times the discount factor, and it is high in the states in which investors most value a payoff.
أمثلة
Example 1.9 (A binomial market)
A bond costs 0.98 and pays 1; a share costs 100 and pays 120 or 90. The equations and give , , both positive: no arbitrage. The risk-neutral probability of the up state is , whatever its real-world probability. A call struck at 100 pays and is worth .