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.
This paper develops a closed-form option valuation formula for a spot asset whose variance follows a GARCH (p, q) process that can be correlated with the returns of the spot asset. It provides the first readily computed option formula for a random volatility model that can be estimated and implemented solely on the basis of observables. The single lag version of this model contains Heston's (1993) stochastic volatility model as a continuous-time limit. Empirical analysis on S&P500 index options shows that the out-of-sample valuation errors from the single lag version of the GARCH model are substantially lower than the ad hoc Black-Scholes model of Dumas, Fleming and Whaley (1998) that uses a separate implied volatility for each option to fit to the smirk/smile in implied volatilties. The GARCH model remains superior even though the parameters of the GARCH model are held constant and volatility is filtered from the history of asset prices while the ad hoc Black-Scholes model is updated every period. The improvement is largely due to the ability of the GARCH model to simultaneously capture the correlation of volatility with spot returns and the path dependence in volatility.
This article discusses the effects of credit market competition on a bank's incentive to keep its commitment to lend to a borrower when the borrower's credit quality deteriorates. It is shown that, unlike in the borrower's commitment problem to keep borrowing from the same bank in "good" times, the increased competition may strengthen a bank's incentive to keep its commitment. Banks offer loans with commitment to the highest quality borrowers but, when faced with competition from bond markets, they also give these loans to lower quality borrowers. An increase in the number of banks has a non-monotonic effect; new banks reinforce a bank's incentive only if there are small number of banks.
The valuation of debt and equity, reorganization boundaries, and firm's optimal dividend policies are studied in a framework where we model strategic interactions between debt holders and equity holders in a game-theoretic setting which can accommodate varying bargaining powers to the two claimants. Two formulations of reorganization are presented: debt-equity swaps and strategic debt service resulting from negotiated debt service reductions. We study the effects of bond covenants on payout policies and distinguish liquidity-induced defaults from strategic defaults. We derive optimal equity issuance and payout policies. The debt capacity of the firm and the optimal capital structure are characterized.
We show that concentrating bank regulation on bank capital ratios may be ineffective in controlling risk taking. We propose, instead, a more direct mechanism of influencing bank risk-taking incentives, in which the FDIC insurance premium scheme incorporates incentive features of top-management compensation. With this scheme, we show that bank owners choose an optimal management compensation structure that induces first-best value-maximizing investment choices by a bank's management. We explicitly characterize the parameters of the optimal management compensation structure and the fairly priced FDIC insurance premium in the presence of a single or multiple sources of agency problems.
This article reports an asset market experiment in which asymmetrically informed traders transact through competing dealers. Dealers face a classic adverse selection problem, because some traders have private information regarding the asset value while other traders are uninformed. When dealers cannot communicate outside the market, they price the asset competitively and the market is generally informationally efficient. When dealers communicate privately between periods, they collude successfully to widen spreads and increase profit. Another treatment permits traders to post limit orders, while still allowing dealers to communicate. Limit orders restore informational efficiency and narrow spreads but cause dealers to earn negative trading profits.
This article develops an efficient and accurate method for numerical evaluation of the integral equation which defines the American put option value function. Numerical integration using Gaussian quadrature and function approximation using Chebyshev polynomials are combined to evaluate recursive expectations and produce an approximation of the option value function in two dimensions, across stock prices and over time to maturity. A set of such solutions results in a multidimensional approximation that is extremely accurate and very quick to compute. The method is an effective alternative to finite difference methods, the binomial model, and various analytic approximations.
We view debt and outside equity as serving to elicit credible information from different specialists about the value of an enterprise in its various uses. The equity valuation specialist provides a price forecast for equity that reveals information about the value of the enterprise in its primary use. The debt valuation specialist provides a price forecast for debt that reveals information about the value of the enterprise in its alternative use. The prices forecast by the valuation specialists credibly reveal their private information because they are required to buy the associated claims at the forecast prices, thereby bonding their valuations.
This study compares the market value of firms that reorganize in bankruptcy with estimates of value based on management's published cash flow projections. We estimate firm values using models that have been shown in other contexts to generate relatively precise estimates of value. We find that these methods generally yield unbiased estimates of value, but the dispersion of valuation errors is very wide-the sample ratio of estimated value to market value varies from less than 20% to greater than 250%. Cross-sectional analysis indicates that the variation in these errors is related to empirical proxies for claimholders' incentives to overstate or understate the firm's value.
This article investigates which companies finance themselves through intermediaries and which borrow directly from arm's length investors. Our empirical results show that large companies with abundant cash and collateral tap credit markets directly; these markets cater to safe and profitable industries, and are most active when riskless rates or intermediary earnings are low. We show that determinants of lender selection sharpen during investment downturns and that there are substantial asymmetries in the way firms enter and exit capital markets. These results support a theoretical framework where intermediaries have better reorganizational skills but a higher opportunity cost of capital than bondholders.