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# 004 Valuing Cash Flows

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### 004 Valuing Cash Flows

1. 1. The Derivatives VALUING CASH FLOWS SKOOL COMPUTER EDUCATION
2. 2. Introduction to State Prices <ul><li>Consider a world that can be in two distinct states tomorrow. </li></ul><ul><li>The realization of tomorrow's state affects the agent's utility, not necessarily in a financial way. </li></ul><ul><li>We will denote for convenience the two states with u-standing for 'up', and d-standing for 'down'. </li></ul><ul><li>We also make the assumption that if the agent could choose tomorrow's state, she would choose 'up'. For example, such states could be </li></ul>
3. 3. Introduction to State Prices <ul><li>It is important to observe that we have not mentioned at all the probabilities of ending up 'up' or 'down' tomorrow . </li></ul>
4. 4. Introduction to State Prices
5. 5. THE PREFERENCES <ul><li>Suppose that the agents utility, which has to be state dependent, is of the standard form, illustrated in figure </li></ul><ul><li>The utility has to be increasing and concave. </li></ul>
6. 6. THE PREFERENCES <ul><li>The money the agent looses if the state is 'down' is the same as the money she would make if the state was 'up'. </li></ul><ul><li>Also assume that the probabilities are equal, in order to eliminate the aforementioned likelihood effect. </li></ul><ul><li>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. </li></ul><ul><li>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. </li></ul>
7. 7. THE PREFERENCES
8. 8. THE PREFERENCES
9. 9. THE PRICING KERNEL
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