an efficient and accurate lattice for pricing derivatives under a jump-diffusion process
Derivatives are popular financial instruments that play essential roles in financial markets. However, most derivatives have no analytical formulas and must be priced by numerical methods such as lattice models. The pricing results generated by a lattice converge to the theoretical values, but they may converge slowly or even oscillate significantly due to the nonlinearity error. According to empirical studies, a lognormal diffusion process, which has been widely studied, does not capture the real world phenomena well. To address these problems, this paper proposes a novel lattice under the jump-diffusion processes. Our lattice is accurate because it suppresses the nonlinearity error. It is more efficient due to the fact that the time complexity of our lattice is lesser than those of the other existing lattice models. Numerous numerical calculations confirm the superior performance of our lattice model to the other existing methods.
jump-diffusion process complexity pricing algorithm