This equation uses the Gauss-Legendre quadrature to approximate the value of a spread option. The Gauss-Legendre quadrature abscissas (Xi) are rescaled in the range -4 to +4. The equation is unbiased and gives very accurate results, typical 6 digit accuracy with 16 quadrature points. The method was describes by K. Ravindran in his paper "Low-fat spreads" (1993) RISK 6 (10) 56--57.
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Price of the spread call option with payoff max(S1-S2-X,0)
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Price of a Black & Scholes vanilla option
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Gauss-Legendre quadrature weights
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Gauss-Legendre quadrature abscissas in the range -4 to +4
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Value of the long underlying
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Volatility of the long underlying
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Yield of the long underlying
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Value of the short underlying
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Volatility of the short underlying
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Yield of the short underlying
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Correlation between the underlyings
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X
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Strike
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t
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Time till expiration
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Normal density function |
