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.

A 4 ML Ni∕W(110) substrate is used to establish a (111) face-centered-cubic (fcc) template upon which 3 ML of Fe is deposited and annealed to 580K to form a substrate with very good short and long range fcc (111) order, that is Fe rich at the surface. Mn alloy films are formed by annealing a subsequent Mn deposit of 0.3–1.6 ML. Low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), and directional AES show that an ordered alloy is not formed until an annealing temperature of 580K, upon which a multilayer alloy with a P(23×23)R30° LEED pattern is created. The alloy films formed from 0.3 to 0.5 ML of Mn have magnetic properties similar to the FeNi substrate. Hysteresis loops and ac-susceptibility curves measured using the Kerr effect give square loops with a ferromagnetic moment along the in-plane fcc [-211] direction and a Curie temperature TC of about 460K. There is an increase in coercive field likely due to the inhomogeneities introduced by the Mn. Alloy films formed from 0.8 to 1.6 ML of Mn show a marked increase in the width of the susceptibility peak, and a decrease in the peak temperature. The hysteresis loop becomes slanted with a reduced coercive field. The measurements are consistent with a paramagnetic or antiferromagnetic Mn alloy forming an uneven interface within the FeNi film, so that the remaining FeNi film has a wide distribution in TC.

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