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Spread Options
A Fourier transform method for spread option pricing
Spread options are a fundamental class of derivative contract written on multiple assets,and are widely used in a range of financial markets. There is a long history of approximationmethods for computing such products, but as yet there is no preferred approach thatis accurate, efficient and flexible enough to apply in general models. The present paperintroduces a new formula for general spread option pricing based on Fourier analysis of thespread option payoff function. Our detailed investigation proves the effectiveness of a fastFourier transform implementation of this formula for the computation of prices. It is foundto be easy to implement, stable, efficient and applicable in a wide variety of asset pricingmodels.
, T.R.Hurd, Z.Zhou (2009)
Analytic Approximations for Spread Options
Even in the simple case that two price processes follow correlated geometric Brownian motions with constant volatility no analytic formula for the price of a standard European spread option has been derived, except when the strike is zero in which case the option becomes an exchange option. This paper expresses the price of a spread option as the price of a compound exchange option and hence derives a new analytic approximation for its price and hedge ratios. This approximation has several advantages over existing analytic approximations, which have limited validity and an indeterminacy that renders them of little practical use. Simulations quantify the accuracy of our approach and demonstrate the indeterminacy and inaccuracy of other analytic approximations. The American spread option price is identical to the European option price when the two price processes have identical drifts, and otherwise we derive an expression for the early exercise premium. A practical illustration of the model calibration uses market data on American crack spread options.
, C.Alexander, A.Venkatramanan (2007)
PRICING AND HEDGING SPREAD OPTIONS IN A LOG-NORMAL MODEL
This paper deals with the pricing of spread options on the difference between correlatedlog-normal underlying assets. We introduce a new pricing paradigm based on a set of precise lowerbounds. We also derive closed form formulae for the Greeks and other sensitivities of the prices. Indoing so we prove that the price of a spread option is a decreasing function of the correlation parameter,and we analyze the notion of implied correlation. We use numerical experiments to provide an extensiveanalysis of the performance of these new pricing and hedging algorithms, and we compare the resultswith those of the existing methods.
, R.Carmona, V.Durrleman (2000)
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