Affine過程の表現公式と部分積分公式

抄録

Affine processes occupy a central role in mathematical finance and other applied fields due to their tractable structure. This article develops probabilistic representation formulas and integration-by-parts identities for expectations of affine processes. A defining feature of the resulting expressions is that they can be written as expectations of affine processes with suitably shifted parameters. The derivations rely on Fourier analysis and characteristic functions, rather than pathwise differentiability, thereby enabling the treatment of affine diffusion models across a wide range of parameter regimes. These identities are well suited for stable Monte Carlo evaluation, as derivatives are reduced to standard expectations under parameter shifts. To illustrate the approach, the formulas are applied to the Cox–Ingersoll–Ross interest rate model, where differentiation with respect to the initial value corresponds to a Greek (delta) in option pricing. The framework provides a unified and robust tool for settings in which classical Malliavin calculus is difficult to apply.