Capital structure arbitrage and market timing under uncertainty and trading noise

ABSTRACT Classical structural models of a firm’s equity and debt are based on the assumption that the price of claims on the firm’s assets depends solely and uniquely on a set of underlying state variables such as the market value of the firm’s assets, as well as claim-specific features such as maturity, callability, etc. We present a model that is based on the alternative notion that participants in the equity and debt markets may disagree on their valuation methodology, introducing uncertainty in the price of claims on the firm’s assets in addition to the uncertainty generated by changes in the assets. In our more general case we show that the introduction of trading noise in the equity and debt markets interferes with arbitrage and hedging strategies and can create potential capital structure arbitrage opportunities. Because we use general jump processes to describe equity and debt prices, we introduce a novel mathematical derivation that is based on a forward-looking, singular perturbation analysis of the joint distribution of the firm’s assets, equity and debt based on multiple time scales.