Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants

A. Bensoussan, M. Crouhy and D. Galai

Applied Mathematical Finance, 1995, vol. 2, issue 1, 43-60

Abstract: We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firm's asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. 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. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firm's total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firm's assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model.

Keywords: corporate finance; financial structure; leverage effect; option pricing; security valuation; stochastic volatility; warrants; numerical methods (search for similar items in EconPapers)
Date: 1995
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Downloads: (external link)
http://www.tandfonline.com/doi/abs/10.1080/13504869500000003 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:apmtfi:v:2:y:1995:i:1:p:43-60

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/RAMF20

DOI: 10.1080/13504869500000003

Access Statistics for this article

Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger

More articles in Applied Mathematical Finance from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().