Capital Structure Effects on Prices of Firm Stock Options: Tests Using Implied Market Values of Corporate Debt

Abstract

This paper introduces a new methodology for measuring and analyzing capital structure effects on option prices of individual firms in the economy. By focusing on individual firms we examine the cross sectional effects of leverage on option prices. Our methodology allows the market value of each firm's debt to be implied directly from two contemporaneous, liquid, at-the-money option prices without the use of any historical price data. We compare Geske's parsimonious model to the alternative models of Black Scholes (BS) (1973), Bakshi, Cao, and Chen (BCC, 1997) (stochastic volatility (SV), stochastic volatility and stochastic interest rates (SVSI), and stochastic volatility and jumps (SVJ)), and Pan (2002) (no-risk premia (SV0), volatility-risk premia(SV), jump-risk premia (SVJ0), volatility and jump risk premia (SVJ)) which allows state-dependent jump intensity and adopts implied state-GMM econometrics. These alternative models do not directly incorporate leverage effects into option pricing, and except for Black-Scholes these model calibrations require the use of historical prices, and many more parameters which require complex estimation procedures. The comparison demonstrates that firm leverage has significant statistical and economic cross sectional effects on the prices of individual stock options. The paper confirms that by incorporating capital structure effects using our methodology to imply the market value of each firm's debt, Geske's model reduces the errors pricing options on individual firms by 60% on average, relative to the models compared herein (BS, BCC, Pan) which omit leverage as a variable. However, we would be remiss in not noting that after including leverage there is still room for improvement, and perhaps by also incorporating jumps or stochastic volatility at the firm level would result in an even better model.

Keywords: Derivatives, Options, Leverage, Stochastic Volatility

JEL Classification: G12