How to evaluate the Fair value of insurance contract has been a popular research subjects since the roaring eighties which caused several insurance companies go bankruptcy (see Briys and de Varenne (1994) for detailed description). Since then, the insolvency risk of insurance company has become a non-ignorable issue. However, the history repeated itself, the Financial Tsunami happened in 2008, not only the insurance companies but also financial service institution. It was mainly because of the low-rate government policy and over credit expansion which is caused by mortgage derivative and high leverage operation. Both fair valuation of complicated derivative and insurance contract are not an easy job. Until now, accounting tends to make the assets and liabilities fairly presented to its fair value in each account. IFRS 4 is an insurance contract accounting standard which is put into practice by most of European Countries like England, German and France. The soul in the accounting standard promote insurance contracts should be presented in fair value on balance sheet; moreover, any embedded options should be take into consideration, and the future cash flow should be discounted under current interest rate. To deal with the tremendous works, there are two phase to go. In phase1, the life insurance companies require a test for the adequacy of recognized insurance liabilities and an impairment test for reinsurance assets; in phase 2, each contract should be discounted under current interest rate and any options embedded should be considered. The first phase is ongoing during 2005 by EU member countries and there are more and more countries follow. The second phase is started off by seldom countries like England and Dutch. To see the effect of IFRS 4 made, we can glimpse into Taiwan’s insurance market.
There have been four European insurance companies sold their business to Taiwan local company since 20071; by year, they are ING Group (2007),
1 Taiwan insurance industry hasn’t follow IFRS 4 standard second phase yet, but will put into practice at 2011.
TransGlobe Life Insurance Inc. (2009), American International Group (2009), and Prudential Assurance Company Limited (2009). Not including American International Group into consideration since the main reason it sell its business to Taiwan local company might be caused by Financial Tsunami. All other insurance companies come from Europe – Dutch and England. They cannot afford high interest spread loss of insurance contracts in Taiwan business since the high technical rate guarantee in early year. Under IFRS4, they are recognized as loss in liabilities.
1.1 Literature Reviews and Motivations
Participating contracts is a popular product when current interest rate is low and expect it will surge up in the future since it participate insurance company’s profit. Thus, even though the technical rate is restricted in low level but there is possible future benefits for policyholder to share. We call this basic option in participating contract as bonus option. Besides bonus option, there are another embedded options covered in the participating contracts, such as surrender option, default option, etc. Surrender option can be seeing as American option which gives the policyholder the right to early exercise the contracts before maturity. In practice, the surrender option involved punishment when policyholder surrender the contract, i.e., it won’t return all the premium you had paid. Bonus option has the main feature of participating contract which mentioned before. When the profit is greater than the interest rate guarantee, policyholder has the right to participate insurance company’s profit. There are several ways to receive the bonus, such as, paid-up insurance premium, save-in agreed interest rate and paid-up additions. In this analysis, we use the paid-up additions form to calculate the future bonus since our framework is mainly focus on single premium insurance. However, in spite of it is an attractive feature to attract policyholder buying the contract, insurance company started cutting their bonuses in order to ensure its survival. At last, default option is the right for policyholder to protect himself from insurance company’s financial distress.
When insurance company suffers insolvency (i.e. company’s assets are not enough to cover its liabilities), policyholder can liquidate residual asset of insurance company. These three options are always considered by most of papers (Bacinello et al., 2003a, 2003b, 2009; Grosen et al., 2000, 2001, 2002;
Chen and Suchanecki, 2007, etc.). Some of these papers consider mortality risk in the framework (Bacinello , Biffis and Millossovich (2009), Bacinello (2003a, 2003b); Grosen, Jensen and Jorgensen (2001)), and some consider default risk (Chen and Suchanecki (2007), Grosen, Jensen and Jorgensen (2002)). , but none of them considers both mortality risk and default risk. In this analysis, we combine both of them and use Parisian option mechanism to construct default option. We allow policyholder liquidate insurance company’s assets if insurance company suffer insolvency for a continue period or cumulative period. This idea is come up by the American bankruptcy law – Chapter 11. Chapter 11 allows insurance company a grace period to reorganize the company before it is liquidated. A company survives if it walks through financial distress or else it goes bankrupt. Such a bankruptcy procedure with a given “grace” period does not only exist in the United States, but also in Japan and in France. Table 1 provides detailed information on the bankruptcy procedure and the number of days spent in default for some exemplary bankruptcies of life insurance companies in the United States.
Table 12
Some defaulted insurance companies in the United States
American defaulted companies Year Bankruptcy code Days spent in default
Executive Life Insurance Co. 1991 Ch.11 462
First Capital Life Insurance Co. 1991 Ch.11 1669
Monarch Life Insurance Co. 1994 Ch.11 392
ARM Financial Group 1999 Ch.11 245
Penn Corp. Financial Group 2000 Ch.11 119
Conseco Inc. 2002 Ch.11 266
2 The data come from http://www.bankruptcydata.com/ and http://www.chapter11blog.com/.
Metropolitan Mortgage & Securities 2004 Ch.11 n/a
U.S. Insurance Group, LLC 2009 Ch.11 n/a
All American Title Agency, LLC 2009 Ch.11 n/a
So far, there are three kinds of method to calculate the initial value of insurance contract by generate future scenario. They are binomial tree (Bacinello, 2003), finite difference (Grosen and Jorgensen, 2001) and Monte Carlo method (Grosen and Jorgensen, 2000; Bacinello , Biffis and Millossovich, 2009). Each method has each pros and cons. We use Monte Carlo Simulation in this analysis since it is easier to construct a complicated stochastic asset value than finite difference method. Moreover; it’s faster than binomial tree when we are dealing a long-term path-dependent contract. In order to generate a model to fit the real world in a more practical and efficient way, we follow the stochastic process in Bakshi, Cao and Chen (1997) to generate Monte Carlo simulation.
Besides, we use an algorithm similar to Bacinello , Biffis and Millossovich (2009) algorithm 1 to calculate the contract value recursively by LSMC.
1.2 Contribution
Our contribution in this study is three-fold; first, we extend the default option with Parisian option framework to deal with the fact that insurance companies may go bankruptcy. And policyholder can liquidate insurance company’s residual value after insurance company can’t go over the grace period of bankruptcy procedure. Second, we use traditional actuarial method to calculate the actual premium for simulation in a more practical view. Third, in fact, it’s hard to use binomial model or finite difference method to deal with the three dimension stochastic valuation. It’s either wasting of time or too complicated to solve the stochastic differential equation. We use LSMC to simplify the timing and complex math equation problem. In comparison to Bacinello , Biffis and Millossovich (2009), we consider about insurance financial face in our cash flow simulation.
This paper is organized as follows. Section 2 describes the model we use to analyze the contacts and presents the basic modeling framework. We also show the state variable and mortality law we use in this part. In section 3 we demonstrate how contract values can be decomposed into their basic elements.
In section 4 we construct the detailed algorithm of each contract. In section 5 we have numerical result for parameter implication. In section 6 we come to a conclusion and future prospects. In section 7 we have regression formula details for section 4.