The Journal of Finance

Options on Leveraged Equity: Theory and Empirical Tests

Published: 04/18/2012   |   DOI: 10.1111/j.1540-6261.1997.tb02728.x

KLAUS BJERRE TOFT, BRIAN PRUCYK

We develop an option pricing model for calls and puts written on leveraged equity in an economy with corporate taxes and bankruptcy costs. The model explains implied Black‐Scholes volatility biases by relating them to the firm's structural characteristics such as leverage and debt covenants. We test the model by comparing predicted pricing biases with biases observed in a large cross‐section of firms with liquid exchange traded option contracts. Our empirical study detects leverage related pricing biases. The magnitudes of these biases correspond to those predicted by our model. We also find significant pricing biases for firms financed primarily by short‐term debt. This supports our model because short‐term debt introduces net‐worth hurdles similar to net‐worth covenants.

Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads

Published: 07/01/1996   |   DOI: 10.1111/j.1540-6261.1996.tb02714.x

HAYNE E. LELAND, KLAUS BJERRE TOFT

This article examines the optimal capital structure of a firm that can choose both the amount and maturity of its debt. Bankruptcy is determined endogenously rather than by the imposition of a positive net worth condition or by a cash flow constraint. The results extend Leland's (1994a) closed‐form results to a much richer class of possible debt structures and permit study of the optimal maturity of debt as well as the optimal amount of debt. The model predicts leverage, credit spreads, default rates, and writedowns, which accord quite closely with historical averages. While short term debt does not exploit tax benefits as completely as long term debt, it is more likely to provide incentive compatibility between debt holders and equity holders. Short term debt reduces or eliminates “asset substitution” agency costs. The tax advantage of debt must be balanced against bankruptcy and agency costs in determining the optimal maturity of the capital structure. The model predicts differently shaped term structures of credit spreads for different levels of risk. These term structures are similar to those found empirically by Sarig and Warga (1989). Our results have important implications for bond portfolio management. In general, Macaulay duration dramatically overstates true duration of risky debt, which may be negative for “junk” bonds. Furthermore, the “convexity” of bond prices can become “concavity.”