Statistics and Its Interface

Volume 11 (2018)

Number 4

Valuation of guaranteed unitized participating life insurance under GEV distribution

Pages: 603 – 614

DOI: https://dx.doi.org/10.4310/SII.2018.v11.n4.a5

Authors

Haitao Zheng (School of Economics and Management, Beihang University, Beijing, China)

Junzhang Hao (School of Economics and Management, Beihang University, Beijing, China)

Manying Bai (School of Economics and Management, Beihang University, Beijing, China)

Zhengjun Zhang (Department of Statistics, University of Wisconsin, Madison, Wi., U.S.A.)

Abstract

The price of option is affected by high volatilities of asset returns. Normal distribution and geometric Brownian motion cannot characterize leptokurtosis and heavy tails of asset returns, which leads to a biased option pricing. Due to guaranteed unitized participating life insurance contracts typically contain various types of implied options, the contract premium will be significantly biased by distribution assumptions. Considering the economic crisis which may change the distribution, this paper extends valuation method of guaranteed unitized participating life insurance under the generalized extreme value (GEV) distribution. Based on the assumption that the returns follow the GEV distribution, we establish a multi-factor fair valuation pricing model of guaranteed unitized participating life insurance contract. It can explicitly capture the negative skewness and the excess kurtosis of asset returns. We study effects of different factors on embedded option values and calculate different annual premiums. The Least-Squares Monte Carlo simulation method is used to simulate the pricing model. Finally, we compare the parameter sensitivity under the GEV and Normal asset returns.

Keywords

generalized extreme value distribution, guaranteed unitized participating life insurance, option pricing, Monte Carlo method

2010 Mathematics Subject Classification

Primary 60G70, 91B30. Secondary 97M30.

Full Text (PDF format)

This work was financially supported by the National Natural Science Foundation of China (grant numbers 71371021, 71333014, 71571007). The first author would also like to thank the supports of Humanities and Social Sciences Planning Fund of Ministry of Education (Grant No. 17YJA790097).

Received 24 August 2017

Published 19 September 2018