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 &amp; 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 reinsurance, 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.

Underwriting Fees and Power Derivatives / Barone, Emilio; Castagna, A.. - (2004). [10.2139/ssrn.512545]

### Underwriting Fees and Power Derivatives

#### 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 reinsurance, 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.
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2004
Underwriting Fees and Power Derivatives / Barone, Emilio; Castagna, A.. - (2004). [10.2139/ssrn.512545]
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11385/168276`
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