On the valuation of American call options on stocks with known dividends

Both the Roll and the Geske equations for the valuation of the American call option on a stock with known dividends are incorrectly specified. This note presents the corrected valuation formula, explains the misspecifications and provides a numerical example.     

An analytic valuation formula for unprotected American call options on stocks with known dividends

Sometimes it pays to exercise an American-type call option prematurely, just prior to a cash emission by the underlying security. Such an option can be expressed as a combination of three European-type options whose valuation formulae are known.     

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

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

Confined exponential approximations for the valuation of American options

We provide an alternative analytic approximation for the value of an American option using a confined exponential distribution with tight upper bounds. This is an extension of the Geske and Johnson compound option approach and the Ho et al. exponential extrapolation method. Use of a perpetual American put value, and then a European put with high input volatility is suggested in order to provide a tighter upper bound for an American put price than simply the exercise price. Numerical results show that the new method not only overcomes the deficiencies in existing two-point extrapolation methods for long-term options but also further improves pricing accuracy for short-term options, which may substitute adequately for numerical solutions. As an extension, an analytic approximation is presented for a two-factor American call option.     

Valuation of American options under the CGMY model

In the present work, we concentrate on the analytical study of American options under the CGMY process. The decomposition formula of the American option and the integral equation for the optimal-exercise boundary are established in explicit forms. Moreover, an analytical approximation formula is obtained for the American value. This approximation is valid when time to maturity is either very short or very long. Numerical simulations are provided for European options, optimal-exercise prices and approximate values for American options.     

Call Completeness Implies Completeness in the n-period Model of a Financial Market

In this paper an arbitrage-free n-period model of a financial market with a predictable, strictly positive numéraire and g risky assets is considered. Complete financial markets are of great practical relevance and of considerable theoretical interest, because in these markets one can find hedging strategies and unique arbitrage-free prices. In this paper complete financial markets are characterized by the simple condition of “call-completeness”.     

A Note on Credit Risk of Vertical <Emphasis Type="Italic">Keiretsu</Emphasis> Firms: Preliminary Evidence from the Japanese Automobile Industry

This paper empirically examines the relationship between the credit risk of Toyota, Nissan and Honda keiretsu-affiliated firms and the credit risk of the respective parent company. As credit spread data for keiretsu-affiliated firms were not available we create a keiretsu default index, as a proxy, using expected default probabilities obtained from the KMV and Leland and Toft (J. Finance 51, 987–1019, 1996) option pricing models. We find parent credit spreads do not Granger cause our keiretsu default index and vice versa in a bivariate vector autoregressive (VAR) framework.JEL classification: G3, L62