Consumption-Based CAPM and Option Pricing under Jump-Diffusion Uncertainty
2003-04
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Consumption-Based CAPM and Option Pricing under Jump-Diffusion Uncertainty
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2003-04
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Center for Economic Research, Department of Economics, University of Minnesota
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Working Paper
Abstract
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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Previously Published Citation
Kusuda, K., (2003), "Consumption-Based CAPM and Option Pricing under Jump-Diffusion Uncertainty", Discussion Paper No. 317, Center for Economic Research, Department of Economics, University of Minnesota.
Suggested citation
Kusuda, Koji. (2003). Consumption-Based CAPM and Option Pricing under Jump-Diffusion Uncertainty. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/55884.
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