A closed-form Random Field solution

Again we show that the transform takes the exponential affine form 

Applying the complex Ito calculus and collecting stochastic and deterministic terms leads to 

6 Multiple-Random Fields term structure models 

Note that we obtain the identical characteristic functions as in section (5.2.1). The new formula for the RF model differs from the corresponding HJM-model only in the variance 

The variance is now extended by the correlation function cj) j. Therefore, using the deterministic volatility function a (r, T) together with the correlation 

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