Classic option pricing theory values a derivative contract via dynamic delta hedging and treating the contract as redundant relative to the underlying security. Dynamic delta hedging proves highly effective in practice, but the remaining risk is still large because of the practical limits of arbitrage. Derivatives can play primary roles in risk allocation. This paper quantifies the percentage variance reduction of delta hedging on U.S. stock options, proposes a top-down return attribution framework to identify the remaining risk sources of the delta-hedged option investment, and constructs a statistical return factor model to explain the variations of the delta-hedged option returns.

Classic bond pricing centralizes bond valuation across all maturities by specifying the dynamics of the short-term interest rate. This article develops a decentralized theory that prices each bond based purely on the near-term behavior of the bond’s own yield. The theory levers the domain expertise of an investor on a particular bond and allows the investor to make pricing and investment analysis on the bond without the shackles of an ambitious centralizing mandate. The theory decomposes the short-term return on a bond with respect to the variation of its own yield. Imposing no dynamic arbitrage on the return decomposition leads to a simple pricing equation relating the bond yield to the market pricing and conditional mean and variance forecasts of the yield’s near-term change. The article illustrates the theory’s applications in decentralized investment of a single bond and in the construction and investment of decentralized butterfly bond portfolios.