Pricing options on leveraged equity with default risk and exponentially increasing, finite maturity debt

We extend a modular pricing framework proposed by Ericsson and Reneby (Appl. Math. Finance 5 (1998) 143; Stock options as barrier contingent claims, Working Paper, Stockholm School of Economics; The valuation of corporate liabilities: theory and tests, Working Paper, Stockholm School of Economics) to derive a valuation formula for calls on leveraged equity, similar to Toft and Prucyk (J. Finance LII (1997) 1151). In contrast to their derivation via partial differential equations, we choose a more elegant probabilistic approach using change of numeraire techniques. Considerably extending previous firm-value-based option pricing models, our framework features exponentially increasing, finite maturity coupon debt, along with taxes and deviations from absolute priority. It enables us to study effects of debt maturity and debt growth on prices of equity options. Numerical results provide new insights into possible causes for pricing biases of the Black-Scholes formula.