Browsing by Author "Kusuda, Koji"

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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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    Existence, Uniqueness, and Determinacy of Equilibria in Complete Security Markets with Infinite Dimensional Martingale Generator
    (Center for Economic Research, Department of Economics, University of Minnesota, 2002-12) Kusuda, Koji
    There is a strong evidence that most of financial variables are better described by a combination of diffusion and jump processes. Considering such evidence, researchers have studied security market models with jumps, in particular, in the context of option pricing. In most of their models, jump magnitude is specified as a continuously distributed random variable at each jump time. Then, the dimensionality of martingale generator, which can be interpreted as the "number of sources of uncertainty" in markets is infinite, and no finite set of securities can complete markets. In security market economy with infinite dimensional martingale generator, no equilibrium analysis has been conducted thus far. We assume approximately complete markets (Bjork et al. [10] [11]) in which a continuum of bonds are traded and any contingent claim can be approximately replicated with an arbitrary precision. We introduce the notion of approximate security market equilibrium in which an agent is allowed to choose a consumption plan approximately supported with any prescribed precision. We prove that an approximate security market equilibrium in approximately complete markets can be identified with an Arrow-Debreu equilibrium. Then, we present sufficient conditions for the existence of equilibria in the case of stochastic differential utilities with Inada condition, and for the existence, uniqueness, and determinacy of equilibria in the case of additively separable utilities.