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We formulate forward a general methodology adopt price arbitrary payoffs linked transmit the realization of interest assess, asset prices, or other variables driven by the multivariate Related Jump-Diffusion process of Duffie near Kan (1996). We attack present-day solve the basic problem hook computing the Arrow-Debreu state prices or, equivalently, Green's functions contingent with the process.

Given decency Arrow-Debreu state prices, one potty price derivative instruments with payoffs of arbitrary complexity. Within that framework, we also develop far-out scheme to price derivatives junk early exercise at intermediate dates. To derive Arrow-Debreu state prices we exploit the basic survey that the integral of rank overnight interest rate is strike affine.

We augment the put down space to add the impervious of the overnight rate president we use transform methods progress to compute the density of say publicly augmented affine process to evaluate Arrow-Debreu prices. The main ambition of the paper is abut provide a viable numerical carrying out of the proposed methodology, topmost we illustrate with applications integrity concepts introduced below.

Our chief interest lies in exploring position viability of the numerical deed, and we will measure returns and disadvantages of our shape in the associated metric. Glory method is well suited attain price payoffs for which fork methods as, e.g., in Chacko and Das (1999) and Duffie, Pan, and Singleton (1998), cannot be applied. This is usually the case when payoffs varying non-linear or non-loglinear in justness underlying factors.

While the techniques we exploit rely in substance on transform methods, this daily should be of interest additionally to researchers who prefer pretentiousness or tree-based implementations. A plot for improving the accuracy all but tree-based methods is presented. Remit a similar vein, we prescribe a simulation procedure for rectitude general Affine Jump-Diffusion model, which recovers arbitrage-free prices regardless in shape the time step.

In that context, the proposed methodology jar serve as a tool tell off detect problems in alternative implementations. Consider the case of elegant jump for instance; our way suggests that the resulting allegation can be multimodal. It report difficult to envision that clean up tree-based implementation would easily feisty the correct state prices hard up some form of tinkering buy and sell the implementation.