Optimal, Static Hedging for Collateralized Mortgage Obligations

Abstract

Collateralized Mortgage Obligations (CMO) can exhibit different degrees of cash flow variability depend-ing on tranche structure and realized prepayment speeds. In order to have a meaningful comparison across structures and collateral types an Option-Adjusted Spread (OAS) methodology is typically used. While OAS provides an improvement to yield-to-maturity for CMO, it does not always make a good com-parison between structures with differing convexities. We introduce a related methodology which in-volves designing an optimal, static hedge. Our valuation directly takes into account the cost of setting up that hedge and thus appears to more fully take into account the negative convexity of a CMO. Numerical results for a simple, transparent binomial model and for market-calibrated Monte-Carlo simulation are given.