Hampus Engsner: The value and replicating portfolio of a liability cash flow in discrete time

Abstract:
Given a liability cash flow, a set of financial replication instruments, including a numeraire asset, and a dynamic monetary risk measure, we derive a replicating portfolio whose market price is taken as the definition of the value of the liability cash flow. This replicating portfolio includes a specific book-keeping strategy for the position in the numeraire asset throughout the runoff of the liability. We show that, under natural conditions, the value of the liability coincides with a value obtained from multi-period valuation using cost-of-capital arguments.