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Equity Options, Credit Default Swaps and Leverage: A Simple Stochastic-Volatility Model for Equity and Credit Derivatives

24 Pages Posted: 1 May 2011 Last revised: 14 Feb 2012

Gaia Barone

LUISS Guido Carli, Department of Business and Management

Date Written: June 2011

Abstract

The aim of this paper is to extract credit-risk sensitive information from the quotes of equity options and CDSs. In particular, we wish to estimate the firm’s leverage, as it is perceived by traders. This goal is achieved within a model à la Leland (1994), where stockholders have a perpetual American option to default. After making the case for modeling debt in terms of a single perpetual-bond equivalent issue, we define leverage, show the stochastic nature of equity volatility and derive the term structures of default probabilities and credit spreads by making use of the first-passage time distribution function. Then, we give new formulas for call and put options written on stockholders’ equity. The formulas, which depend on the leverage parameter L and make use of the univariate normal distribution function, are consistent with the volatility skew observed in the equity options market and converge to the Black-Scholes-Merton (BSM) equations for L → 1. All the Greeks are simple functions of the standard corresponding letters of the BSM model. The paper concludes with an application of the model to the case of Lehman Brothers and General Motors.

Keywords: equity options, credit default swaps, leverage, stochastic volatility, perpetual options, first-touch digitals, Greeks, default probabilities, put-call parity

JEL Classification: G13

Suggested Citation

Barone, Gaia, Equity Options, Credit Default Swaps and Leverage: A Simple Stochastic-Volatility Model for Equity and Credit Derivatives (June 2011). Available at SSRN: https://ssrn.com/abstract=1826019 or http://dx.doi.org/10.2139/ssrn.1826019

Gaia Barone (Contact Author)

LUISS Guido Carli, Department of Business and Management ( email )

Viale Romania, 32
Rome, Rome 00197
Italy

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