Divergent interest rates in the theory of financial markets

Abstract

We extend models of financial markets by incorporating divergent risk-free interest rates for borrowing and deposits. Divergent interest rates create arbitrage opportunities if each market participant is allowed both to borrow and lend money. In our model, we circumvent such arbitrage opportunities by allowing only one institution to act as a bank (granting risk-free credits and financial investments). The surplus of this bank has to be redistributed to the market participants.

Assuming only one risky asset we show that – while not necessarily unique – an equilibrium always exists. We investigate the relation to a financial markets equilibrium based on a unique interest rate being intuitively determined as a (weighted) average from borrowing and deposit rate. We provide proof that this unique interest rate approximately generates correct asset prices only if every investor trades, the bank's proceeds are distributed equally among investors and the number of investors is rather large. Otherwise severe mispricings may result.