Abstract. Spread options are a fundamental class of derivative contracts written on multiple assets and are widely traded in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is no preferred approach that is accurate, efficient, and flexible enough to apply in general asset models. The present paper introduces a new formula for general spread option pricing based on Fourier analysis of the payoff function. Our detailed investigation, including a flexible and general error analysis, proves the effectiveness of a fast Fourier transform implementation of this formula for the computation of spread option prices. It is found to be easy to implement, stable, efficient, and applicable in a wide variety of asset pricing models.
We study the sine-Gordon model in two dimensional space time in two different domains. For β > 8π and weak coupling, we introduce an ultraviolet cutoff and study the infrared behavior. A renormalization group analysis shows that the the model is asymptotically free in the infrared. For β < 8π and weak coupling, we introduce an infrared cutoff and study the ultraviolet behavior. A renormalization group analysis shows that the model is asymptotically free in the ultraviolet.
We analyze the consumption-portfolio selection problem of an investor facing
both Brownian and jump risks. We bring new tools, in the form of orthogonal
decompositions, to bear on the problem in order to determine the optimal
portfolio in closed form. We show that the optimal policy is for the investor
to focus on controlling his exposure to the jump risk, while exploiting
differences in the Brownian risk of the asset returns that lies in the
orthogonal space.Comment: Published in at http://dx.doi.org/10.1214/08-AAP552 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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