Marco Di Francesco, Sidy Diop, Andrea Pascucci: We propose a new methodology for the calibration of a hybrid credit-equity model to CDS spreads and survival probabilities. We consider an extended Jump to Default Constant Elasticity of Variance model incorporating stochastic and possibly negative interest rates. Our approach is based on a perturbation technique that provides an explicit asymptotic expansion of the CDS spreads. The robustness and efficiency of the method is confirmed by several calibration tests on real market data.
ESR3 Sidy Diop
Marco Di Francesco, Sidy Diop, Andrea Pascucci: We propose a new methodology for the calibration of a hybrid credit-equity model to credit default swap (CDS) spreads and survival probabilities. We consider an extended Jump to Default Constant Elasticity of Variance model incorporating stochastic and possibly negative interest rates. Our approach is based on a perturbation technique that provides an explicit asymptotic expansion of the credit default swap spreads. The robustness and efficiency of the method is confirmed by several calibration tests on real market data.
Gian Luca De Marchi, Marco Di Francesco, Sidy Diop, Andrea Pascucci: Abstract to follow.
M.C. Calvo-Garrido, S. Diop, A Pascucci, C. Vázquez: In this paper, we consider the numerical solution of a two factor model for the valuation of a non callable defaultable bond which pays coupons at certain given dates. Such a model under consideration is the Jump to Default Constant Elasticity of Variance (JDCEV) model. The stochastic factors are the risk free interest rate and the stock price. Moreover, we take into account the possibility of negative interest rates. From the mathematical point of view, the valuation problem requires the numerical solution of two partial differential equation (PDE) problems for each coupon and with maturity those coupon payment dates. In order to solve these PDE problems, we propose appropriate numerical schemes based on a Crank-Nicolson semi-Lagrangian method for time discretization combined with biquadratic Lagrange finite elements for space discretization. Once the numerical solutions of the PDEs are obtained, a kind of post-processing is carried out in order to achieve the value of the bond. This post-processing includes the computation of an integral term which is approximated by using the composite trapezoidal rule. Finally, we present some numerical results for real market bonds issued by different firms in order to illustrate the proper behaviour of the numerical schemes.