Valuation of Insurance Products with Shout Options in a Jump-Diffusion Model

Jun Liu,Zhian Liang,Emilio Gómez-Déniz

doi:10.1155/2021/3948897

Abstract

The insurance product with shout options which permit the holders to modify the contract rules is one of the most popular products in European and American markets today. Therefore, it is of great significance to price more precisely. A new mathematical model consisting of a partial differential inequality and constraint conditions is derived for the price of insurance products in a jump-diffusion model. The numerical experiments are performed to analyze the impact of parameters on the insurance product with shout put options, especially for the jump times and the quantities of shout opportunities. The experiment results show that the value of the product is strongly affected by the quantities of shouting opportunities, especially for high values of the underlying asset, while it is only weakly affected for low values. Meanwhile, another meaningful discovery is that the valuation has changed little as the jump times are less than five, while it has shown a sharp increase once the jump times are more than five. Furthermore, the indicator results of course grid errors show that the values of shout put options in the jump-diffusion model are more accurate than those in a Brownian motion.

Highlights

One of the most popular investments in European and American markets today is the insurance product containing shout options that permit the holders to modify the rules within the contract life. erefore, it is meaningful to price as accurately as possible.e academic research on pricing shout options has been extensive. omas [1] described the context of shout put and call options
We have presented a new mathematical model in a jump-diffusion process to price the insurance products with shout options more accurately. e value of these types of contracts can be estimated by solving a differential-difference inequality with minimum constraint conditions, which originate from the unique feature of shout options
Compared with the previous models’ shout options in a Brownian motion, the new model in this paper takes into account jump phenomenon of the underlying asset price and the unique feature which permits the holder to transform the contract for another

Summary

Introduction

One of the most popular investments in European and American markets today is the insurance product containing shout options that permit the holders to modify the rules within the contract life. erefore, it is meaningful to price as accurately as possible. GhodssiGhassemabadi and Yari [13] proposed a multilevel Monte Carlo approach for the valuation of swing options, which are related with shout options In these papers, shout options were valuated based on a Brownian motion and constant volatility of the underlying asset price. E objective of this article is to propose a new mathematical model that can be used to value insurance products with shout options, while making an assumption about a jump-diffusion model followed by the underlying asset.

The Mathematical Model

Numerical Analysis

Result in this paper

Conclusions