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The DerivativesVALUING CASH FLOWS

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SKOOL COMPUTER EDUCATION

Introduction to State Prices

• Consider a world that can be in two distinct states tomorrow.

• The realization of tomorrow's state affects the agent's utility, not necessarily in a financial way.

• We will denote for convenience the two states with u-standing for 'up', and d-standing for 'down'.

• We also make the assumption that if the agent could choose tomorrow's state, she would choose 'up'. For example, such states could be

SKOOL COMPUTER EDUCATION

Introduction to State Prices

• It is important to observe that we have not mentioned at all the probabilities of ending up 'up' or 'down' tomorrow.

SKOOL COMPUTER EDUCATION

Introduction to State Prices

SKOOL COMPUTER EDUCATION

THE PREFERENCES• Suppose that the agents utility, which has to be state dependent, is of the standard form, illustrated in figure

• The utility has to be increasing and concave.

SKOOL COMPUTER EDUCATION

THE PREFERENCES

• The money the agent looses if the state is 'down' is the same as the money she would make if the state was 'up'.

• Also assume that the probabilities are equal, in order to eliminate the aforementioned likelihood effect.

• Even in this [perfectly symmetric] case, the special utility shape implies that the absolute utility changes are not equal: The drop of the utility in the 'down' state is higher than the utility gains in the 'up' state.

• A rational agent would therefore value the 'down' state with a higher state price: more money would be happily paid out in order to ensure a higher consumption in the 'down' state.

SKOOL COMPUTER EDUCATION

THE PREFERENCES

SKOOL COMPUTER EDUCATION

THE PREFERENCES

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THE PRICING KERNEL