Robert Geske

The valuation of compound options

This paper presents a theory for pricing options on options, or compound options. The method can be generalized to value many corporate liabilities. The compound call option formula derived herein considers a call option on stock which is itself an option on the assets of the firm. This perspective incorporates leverage effects into option pricing and consequently the variance of the rate of return on the stock is not constant as Black-Scholes assumed, but is instead a function of the level of the stock price. The Black-Scholes formula is shown to be a special case of the compound option formula. This new model for puts and calls corrects some important biases of the Black-Scholes model.

A note on an analytical valuation formula for unprotected American call options on stocks with known dividends

Abstract This note provides simple analytic formulas for the value of an American call option on a stock with known dividends.

Valuation by Approximation: A Comparison of Alternative Option Valuation Techniques

The purpose of this paper is to compare a variety of approximation techniques for valuing contingent contracts when analytic solutions do not exist. The comparison is made with respect to the differences in both the approximation theory and the efficiency of the computation algorithms. The focus of the computational comparison is upon binomial and finite difference methods applied to option valuation models with one stochastic variable. However, many of the results would generalize to pricing corporate securities, and also to certain aspects of problems involving multiple stochastic variables.

Comments on Whaley's note

Abstract Valuation by duplication is a useful conceptual technique but it does not yield unique formula. Many duplicating portfolios, some simpler than the three security portfolio in Roll and Whaley, exist for this problem. Valuing the actual single security will generally yield conceptually and computationally simpler solutions.

The early exercise of American puts

Abstract This paper shows that American puts on dividend paying stocks are most likely to be exercised either just after an ex-dividend date or just prior to expiration. At any other time the option to exercise an American put early may have less value. Thus, put writers and converters can predict when protection against premature exercise will be most valuable. The probability of early exercise is shown to be sensitive to managerial policy regarding the suspension of dividend payments, transaction costs, and interest rates. However, dividend payments are demonstrated to be the primary deterrent to early exercise.

Mutual fund insurance

Abstract During the 1970s, mutual fund insurance was sold in the U.S. by the Harleysville and Prudential Insurance Companies. This paper examines the valuation and demand for this insurance. It illustrates that because of its design, for many plausible combinations of model parameters, a competitive premium need not exist for the Harleysville contract. A competitive premium will always exist for the Prudential policy, however the value is directly related to the age of the purchaser. Harleysville charged the same premium to all funds and therefore was subject to adverse selection. Evidence of this effect is provided by illustrating that the demand for the insurance was directly related to its competitive market value.

Capital Structure Effects on the Prices of Individual Equity Call Options

We examine whether values of equity options traded on individual firms are sensitive to the firms capital structure. Specifically, we estimate the compound option (CO) model, which views equity as an option on the firm. Compared to the Black-Scholes (BS) model, the CO model reduces pricing errors by 20% on average, and pricing improvements monotonically increase up to 70% with both leverage and expiration. We show that the CO model implies a market value of firm leverage and allows imputation of the firms implied volatility, both of which have potential applications in corporate finance.