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Title: Distribution function for cumulative intensity of SSRJD and its applications to CVA of CDS Authors:  Toshinao Yoshiba - Bank of Japan (Japan) [presenting]
Tetsuya Adachi - Financial Services Agency (Japan)
Takumi Sueshige - EY Shinnihon LLC (Japan)
Abstract: The shifted square root jump diffusion (SSRJD) is a tractable process for the stochastic default intensity to valuate CDS (credit default swap) incorporating its surge under stress. While a copula approach is a promising way to evaluate the CVA (credit valuation adjustment) of a CDS with a wrong-way risk, the distribution function for cumulative intensity of SSRJD is needed to apply the copula approach. We show the derivation of the distribution function. Since the SSRJD is an affine process, the characteristic function of cumulative intensity follows Riccati-type ordinary differential equations. The analytic solution can be obtained; however, the solution defined on the space of complex-value is multivalued. We show the way to solve this problem with reducing the multilayered Riemann surface of the solution to a single layer. Applying the fractional fast Fourier transform and numerical integration to the characteristic function of SSRJD cumulative intensity, the distribution function is derived. Using the result, we also show comparative analyses between the copula approach and a co-jump model for counterparty and reference default intensities.