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a b s t r a c tWe extend a framework based on Mellin transforms and show how to modify the approach to value American call options on dividend-paying stocks. We present a new integral equation to determine the price of an American call option and its free boundary using modified Mellin transforms. We also show how to derive the pricing formula for perpetual American call options using the new framework. A result due to Kim (1990) [24] regarding the optimal exercise price at expiry is also recovered. Finally, we apply Gauss-Laguerre quadrature for the purpose of an efficient and accurate numerical valuation.
In this paper we investigate Metallgesellschaft’s problem of hedging long-term forwards with short-term futures. Very different hedging strategies have been proposed in the literature. We attribute these differences to the underlying valuation approaches for oil futures and empirically compare five model-based hedging strategies. In particular, we consider a strategy which results from a two-regime pricing model. This continuous-time equilibrium model reflects the observation that prices of oil futures exhibit a very different behavior for low and high oil prices. Our empirical study shows that time diversification is the dominant effect for an effective hedging of long-term oil forwards with short-term futures. Copyright Kluwer Academic Publishers 2005long-term forwards, hedging, Metallgesellschaft case, two-regime pricing.,
Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Simple formulas for the price of corporate discount and coupon bonds are found using the Longstaff and Schwartz [1995] valuation approach for the debt claims of a firm, where default is triggered by a special State variable: the firm's asset-to-debt-ratio. Instead of keeping the total amount of debt constant over time, it is shown that closed form solutions exist under the alternative assumption that the level of leverage is expected to remain constant over time under the risk-neutralized measure. This encourages a more conservative view on the capital structure policy of the firm which might be appropriate in case the firm is neither Willing nor able to reduce its expected level of leverage considerably over time.
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