Pricing by Arbitrage When All Assets are Risky : A Theory of Latent Interest Rate and Evidence

When a (locally) riskless asset does not trade, the market is necessarily incomplete and the risk-adjusted drift on any traded asset is equal to the drift on the minimum instantaneous variance portfolio, which we call the latent interest rate. Options can still be priced by replication if the drift and volatility coefficients of the underlying assets are homogeneous of degree zero in asset prices and a locally risky pure discount bond with the same maturity trades. Option price data imply that our latent interest rate is significantly different and twenty times more variable (over time) than the observed spot interest rate. Our model does not exhibit the smile effect which is significant within the Black-Scholes model