Browsing by Subject "G11"

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    Consumption-Based CAPM and Option Pricing under Jump-Diffusion Uncertainty
    (Center for Economic Research, Department of Economics, University of Minnesota, 2003-04) Kusuda, Koji
    In Kusuda [45], we developed equilibrium analysis in security market economy with jump-Wiener information where no finite number of securities can complete markets. Assuming approximately complete markets (Bjork et al. [11] [12]) in which a continuum of bonds are traded and any contingent claim can be replicated with an arbitrary precision, we have shown sufficient conditions for the existence of approximate security market equilibrium, in which every agent is allowed to choose any consumption plan that can be supported with any prescribed precision. In this paper, we derive the Consumption-Based Capital Asset Pricing Model (CCAPM) using the framework in case of heterogeneous with additively separable utilities (ASUs) and of homogeneous agents with a common stochastic differential utility (SDU). The CCAPM says that the risk premium between a risky security and the nominal-risk-free security can be decomposed into two groups of terms. One is related to the price fluctuation of the risky security, and the other is related to that of commodity. Each group can be further decomposed into two terms related to consumption volatility and consumption jump in case of ASUs, and into three terms related to consumption volatility, continuation utility volatility, and jumps of consumption and continuation utility in case of SDU. Next, we present a general equilibrium framework of jump-diffusion option pricing models in each case of heterogeneous agents with CRRA utilities and of homogeneous agents with a common Kreps-Porteus utility. Finally, we construct a general equilibrium version of an affine jump-diffusion model with jump-diffusion volatility for option pricing using the framework.
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    Valuation and Asset Pricing in Infinite Horizon Sequential Markets with Portfolio Constraints
    (Center for Economic Research, Department of Economics, University of Minnesota, 1998-10) Huang, Kevin Xiaodong
    There are three ways of measuring the value of a payoff stream in sequential markets with portfolio constraints: the market price, the replication price, and the fundamental value. In this paper we characterize constraints for which these measures coincide in the absence of arbitrage, and in equilibrium. We show that the replication price functional is linear in finite horizon markets, but only sub-linear in general in infinite horizon unless markets are complete. We provide constraints for which the linearity holds regardless whether markets are complete or incomplete. Applying a duality technique, we determine an optimal replicating strategy through solving a sequence of independent linear programs. These results do not depend on investors' preferences (other than monotonicity), probability beliefs, endowments of goods, or supply of assets.