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Ch. 12 The Martingale Measure: Part II

12.3 Risk-Neutral Pricing in the CCAPM. A.12.1There is one agent in the economy with time separable VNM preferences represented bywhere {U(c, t)} is a family of strictly increasing, concave, differentiable period utility functions, is the uncertain period t consumption, and E

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Ch. 12 The Martingale Measure: Part II

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    1. Ch. 12 The Martingale Measure: Part II 12.1 Introduction 12.2 Discrete Time Infinite Horizon Economies: A CCAPM Setting 12.3 Risk-Neutral Pricing in the CCAPM 12.4 The Binominal Model of Derivatives Valuation 12.5 Continuous Time: AN Introduction to the Black-Scholes Formula 12.6 Dybvigs Evaluation of Dynamic Trading Strategies 12.7 Conclusions

    2. 12.3 Risk-Neutral Pricing in the CCAPM A.12.1 There is one agent in the economy with time separable VNM preferences represented by where {U(c, t)} is a family of strictly increasing, concave, differentiable period utility functions, is the uncertain period t consumption, and E0 the expectations operator conditional on date t=0 information.

    3. A.12.2 Output in this economy, is exogenously given , and, by construction, represents the consumers income. In equilibrium it represents his consumption as well.

    5. 12.4 The Binominal Model of Derivatives Valuation At every date-state node, only a stock and a bond are traded. (Dynamic) completeness only two possible succeeding states A.12.3 The risk free rate is constant;

    6. A.12.4 The stock pays no dividends: d(qt) ? 0 for all t ? T. A.12.5 The rate of return to stock ownership follows an i.i.d. process of the form: Absence of arbitrage opportunity => u > Rf > d, where, in this context, Rf = 1 + rf.

    8. Compare with (12.8) . Arrow-Debreu securities:

    9. Example 12.4: A European Call Option Revisited

    11. Define the quantity as the minimum number of intervening up states necessary for the underlying asset, the stock, to achieve a price in excess of E. The above expression can then be simplified to:

    12. Example 12.5

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