Cat bond valuation using Monte Carlo and quasi Monte Carlo method

The frequency of natural disasters is very small, but the loss of damage and the risks that must be borne is of enormous value. Recently, Catastrophe bond (CAT bond) has grown rapidly in financial markets to increase the coverage of environmental disasters and the resulting economic losses, insurance companies and reinsurers are barely covered. Catastrophe bond (CAT Bond) is one of the insurance-linked financial securities instruments that aim to transfer risk by insuring natural disaster events to the capital market. The model of natural disaster loss without a jump-diffusion process followed a model of geometric Brownian motion. We estimate and match each parameter in each model by using grid search and then we use the method of Monte Carlo and quasi-Monte Carlo to obtain numerical results for the CAT bonds pricing formulas. From this simulation, the Monte Carlo method has good enough accuracy and efficiency to valuates the CAT bond. Less then 500 iterations Monte Carlo have reached convergence in 1280.49 seconds. And quasi-Monte Carlo more efficient with less than 400 iterations have reached convergence in 30.89 seconds. Both methods have reached small enough MAPE. Based on the simulations carried out through this research, it was showed that the quasi-Monte Carlo method is better than the Monte Carlo method based on the value of Mean Absolute Percentage Error (MAPE) and running time.