Forward rate dynamics are modeled as a random field. In contrast to multifactor models, random field models offer a parsimonious description of term structure dynamics, while eliminating the self-inconsistent practice of recalibration. The form of the drift of the instantaneous forward rate process necessary to preclude arbitrage under the risk-neutral measure is obtained. Forward risk-adjusted measures are identified and used to price a bond option when the forward volatility structure depends on the square root of the current spot rate. Several classes of tractable random field models are presented.

We revisit Feldhütter and Schaefer (FS, 2018), who report evidence of a “credit spread puzzle” for high-yield but not investment-grade bonds. We show their results are reversed when their model is calibrated to market values of debt (as required by theory) rather than book values. We then demonstrate that using credit spreads rather than historical default rates to identify the default boundary provides the statistical power necessary to reject their assumption that firm dynamics follow geometric Brownian motion. A large market price of jump risk is required to match historical default rates, which generates a credit spread puzzle for investment-grade but not high-yield bonds.

Benchmark models that exogenously specify equity dynamics cannot explain the large spread in prices between put options written on individual banks and options written on the bank index during the financial crisis. However, theory requires that asset dynamics be specified exogenously and that endogenously determined equity dynamics exhibit a “leverage effect” that increases put prices by fattening the left tail of the distribution. The leverage effect is larger for puts on individual stocks than for puts on the index, thus increasing the basket-index spread. Time-series and cross-sectional variation in the leverage effect explains option prices well.