Stochastic equity volatility related to the leverage effect

Alain Bensoussan, Michel Crouhy and Dan Galai

Applied Mathematical Finance, 1994, vol. 1, issue 1, 63-85

Abstract: We propose a general framework to model equity volatility for a firm financed by equity and additional non-equity sources of funds. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities. Second, we show for the first time in the option literature, that instantaneous equity volatility is a solution of a partial differential equation similar to Black-Scholes', although it is non-linear and in general does not have any analytical solution. However, analytical approximations for equity volatility are proposed for different capital structures: (1) equity and debt, (2) equity and warrants, and (3) equity, debt and warrants. They are shown to be very accurate.

Keywords: corporate finance; financial structure; leverage effect; option pricing; security valuation; stochastic; volatility; warrants; numerical methods (search for similar items in EconPapers)
Date: 1994
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Citations: View citations in EconPapers (11)

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DOI: 10.1080/13504869400000004

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