Risk Latte - Sudden Birth or Death Options and Market Downturns

Sudden Birth or Death Options and Market Downturns

Rahul Bhattacharya
Aug 28, 2006

Seldom do people worry about their own deaths and market downturns at the same time. How probable is it that a man will die in the same year that there is a major market downturn? The answer to this rather morbid and disturbing question is that such a probability is low, perhaps quite low. More importantly, with equity markets hitting new highs every day and so much wealth around who could be bothered to think about death and market downturns?

There is a class of options-derivatives-which are little known outside the insurance world, at least the way the nomenclature of these options go. These are called sudden birth/death options. Barrier options, the knock-ins and knock-outs that are extremely popular and enjoy high volumes in the global banking and investment community are actually sudden death/birth options, but rarely do we think of them like that. If the maturity date (the term) of an option in a pricing model, say the Black-Scholes model, becomes non-constant and even stochastic then we get a sudden birth or death options. Sudden birth and death options have been popular.

An example of sudden birth/death options is the GMDBs-Guaranteed Minimum Death Benefits-that have been so popular in the insurance industry for a couple of decades. A GMDB is a principal guaranteed note that are tied to an equity index (or sometimes and interest rate) such as the S&P500, TSE35, DAX, etc.) and has an upside participation. A GMDB is a structured note that expires only when the investor (purchaser of the note/policy) dies. In insurance terms these are called variable annuities, a decidedly a vexing and complex instruments to value. The options embedded in variable annuities are difficult to price and hedge because of the sensitivity of the benefits - payoffs - to the tail distributions of the underlying accounts and their long maturity. In most cases Merton's jump diffusion model is used to value the embedded options in variable annuities.

Now the question we posed at the opening of this article. In the bullish markets of 1990s and especially the late 1990s most insurance companies were happy with selling and managing their GMDBs, but the subsequent market crash in the year 2000 made many companies realize that they could be facing large losses, both on their asset portfolios linked to the equity markets as well as on liability side, where claims could come in due to death of the policy holder. In these circumstances GMDBs very unattractive for the surviving family members of the policyholders and even the insurance companies found them driving a hole through their balance sheets. The problem was further exaggerated because during the bullish decade of 1990s many insurance companies had issued complex ratchet GMDBs which guarantees a death benefit based on the highest anniversary account value (i.e. the highest value of an equity index between a certain period until the death of the policy holder will be taken for calculation rather than the closing value of the index on the date of death of the policyholder).

Who knows with markets touching dizzying heights once again, GMDBs might come back with a vengeance! Or perhaps some insurance companies might come up with innovative solutions using the flip side of the argument. Maybe, now we may have annuity linked policies which come to life - sudden birth - when a certain threshold is breached on the downside by an equity index and a whole of products structured around this idea.

Reference: Hedging Guarantees in Variable Annuities under both Equity & Interest Rate Risk (Thomas Coleman, Yuing Li and Maria-Cristina Patron) and The Handbook of Exotic Options ( Israel Nelken, Irwin Publishing)

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