Underwriting Fees and Power Derivatives

19 Pages Posted: 5 Mar 2004

See all articles by Emilio Barone

Emilio Barone

Luiss - Guido Carli (Dpt. of Economics and Finance)

Antonio Castagna

Iason Ltd.

Date Written: June 1998

Abstract

In this paper we analyze the problem of determining standby underwriting fees within the framework of option-pricing theory. Financial institutions that provide standby underwriting for a stock placement bear the risk of having to buy unplaced stocks if the offered quantity is not completely absorbed by the market. We describe a simple model in which the equilibrium price of the stock at the end of the placement period is log-normal and the demand curve for stocks can shift according to stochastic shocks. We show that the value of the guarantee offered by the financial institutions is proportional to the value of a "quadratic" power put, that is a derivative whose payoff is the square of an ordinary put. This option can be priced within the Black & Scholes theoretical framework. The closed-form formula shows that the value of a quadratic put is much greater than that of an ordinary put and is not simply the square of the latter's value. The paper also analyzes the problem of "re-insurance", which arises when the underwriting fee is partially transferred to another financial institution that provides a subsidiary guarantee. We analyze three different contractual arrangements between two financial institutions, and accordingly show how to allocate the total fee consistently between them. A simulated application of the model is also presented.

Suggested Citation

Barone, Emilio and Castagna, Antonio, Underwriting Fees and Power Derivatives (June 1998). Available at SSRN: https://ssrn.com/abstract=512545 or http://dx.doi.org/10.2139/ssrn.512545

Emilio Barone (Contact Author)

Luiss - Guido Carli (Dpt. of Economics and Finance) ( email )

Viale Romania, 32
Rome, 00197
Italy

HOME PAGE: http://docenti.luiss.it/barone/

Antonio Castagna

Iason Ltd. ( email )

7th Floor, Hume House
Dublin, 4
Ireland

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