Pricing European options under stochastic looping contagion risk model

In this paper, we establish the pricing framework of European options in the presence of the looping contagion risk. First, the looping contagion risk model is transformed into a martingale form and the semi-explicit risk-neutral pricing formula is established for the pricing of European options. Then the pricing partial differential equations (PDEs) are derived and solved by the stable alternating direction implicit (ADI) methods. Moreover, the ADI methods in this paper are proved to be unconditionally stable through Fourier analysis framework. Finally, the Monte Carlo simulations are performed and combined with the numerical solutions of PDEs to compute the desired option prices via the semi-explicit pricing formula. Numerical examples are given to confirm the convergence of the numerical methods and the economic analysis is provided to illustrate the economic effect of the looping contagion risk on option prices.