Pricing of Adverse Development Covers Using Option Pricing Methods

Abstract

The market for Adverse Development Covers and Loss Portfolio Transfer has been growing in the past few years. Despite this growth, reinsurers are still struggling to define a standard method for pricing such covers. In this context, this article aims at providing an innovative method for pricing such contracts. The proposed method is based on the famous Mack model and fits a Constant Elasticity of Variance (CEV) model to the Mack results (expected value and standard deviation) on each future development year of each accident/underwriting year. Having fitted the CEV model, it is possible to estimate the value of the Adverse Development Covers for each accident/underwriting year using standard European option pricing techniques and to compare this valuation with usual Non-Life Insurance valuation techniques.

TOPICS: Derivatives, options, quantitative methods, statistical methods, risk management

Key Findings

• ▪ It is possible to replicate the Mack model estimating the ultimate non–life insurance reserves with a CEV model and to find a good fit for the CEV model.

• ▪ The proposed CEV model seem to provide better results than models based solely on the ultimate view of the non–life insurance reserves.

• ▪ It is important to take into account not only the ultimate volatility of the insurance reserves but also the way in which the volatility develops. Such conclusion matches the usual question of the volatility smile for option pricing techniques.