On incompleteness of bond markets with infinite number of random factors
Micha{\l} Barski, Jacek Jakubowski, Jerzy Zabczyk
TL;DR
This paper demonstrates that bond markets with infinitely many sources of randomness are inherently incomplete, providing a specific example of a claim that cannot be replicated within this framework.
Contribution
It proves the incompleteness of infinite-factor bond markets and constructs a bounded claim that cannot be hedged, advancing understanding of market limitations.
Findings
Market with infinite sources of randomness is incomplete
Existence of unreplicable bounded contingent claims
Inability to replicate certain claims in the model
Abstract
The completeness of a bond market model with infinite number of sources of randomness on a finite time interval in the Heath-Jarrow-Morton framework is studied. It is proved that the market is not complete. A construction of a bounded contingent claim, which can not be replicated, is provided.
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Taxonomy
TopicsStochastic processes and financial applications · Financial Risk and Volatility Modeling · Economic theories and models