(A) new variance reduction, pricing method and model for option and insurance

Abstract

The dissertation contains three main subjects about a new variance reduction, pricing method and model for option and insurance. First, a new variance reduction method for option pricing is introduced which is more efficient than antithetic variates method. Next, a new method for pricing insurance derivative and arithmetic Asian option is suggested in the jump CIR diffusion process using joint Laplace transform. Last, a new contagion model is constructed using Eisenberg-Noe model which is used for obtaining clearing payments.