Options on Leveraged Equity with Default Risk

Klaus Bjerre Toft.

No RPF-238, Research Program in Finance Working Papers from University of California at Berkeley

Abstract: In this paper, I derive option pricing formulas for call and put options written on leveraged equity in an economy with corporate taxes and bankruptcy costs. The firm can be forced into bankruptcy by breaching a net-worth covenant, or it may declare bankruptcy when it is optimal for equity holders to do so. Consequently, option values and sensitivities depend on structural variables such as the corporate tax rate, the firm's coupon payments, and the firm value at which bankruptcy is declared. The derived formulas for calls and puts on equity with default risk simplify to Black-Scholes type formulas for down-and-out barrier options if bankruptcy is declared as soon as the value of the firm's assets equals the after-tax value of the promised coupon payments on the debt. If the capital structure contains no debt, the pricing results simplify to Black-Scholes formulas for call and put options. The model developed in this paper relates implied Black-Scholes volatility for equity options to structural characteristics such as leverage and the debt's protective covenants. Options priced by the proposed model are characterized by Black-Scholes implied volatilities which are decreasing in striking price. Moreover, equity options on firms with protected debt have more pronounced volatility skews than options on firms with unprotected debt. Finally, I show how to evaluate the term structure of default spreads for corporate interest-only strips.

Date: 1994-07-01
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