The Options Embedded within Pension Plans: Types, Valuation Principles and Effects on Optimal Investment Policies
Bankers, Markets & Investors, Forthcoming
Posted: 1 Jun 2010
Date Written: September 27, 2009
Analyzing the options embedded within pension plans constitutes this paper’s first objective. Contingent claims emerge when decomposing the pension scheme payoffs or in the form of defined benefit or defined contribution plan guarantees. A valuation exercise is proposed in a second step, applied to one of the main options encountered : the European-type put option on the fund assets with the strike price equal to liabilities. The novel issue of the liability formulation effects on this put value is raised. Three liability definitions are used - the simple wage mean, the weighted wage mean and the final wage, leading to the emergence of three kinds of exchange options: the standard one and two types of Asian options, with normal and weighted arithmetic averaging. The implementation of the models by means of Monte Carlo simulations shows that, in comparison with the final wage definition, the simple wage mean formulation strongly reduces the sensitivity of the put value to variations in the wage volatility, in the correlation rate between the wage and asset processes and a constant defining the pension benefits, and also increases the sensitivity to the asset volatility. The liability definition thus constitutes one of the factors to consider when assessing the riskiness of the option seller’s position. Finally, the paper focuses on the effects of the options existence on the optimal behavior of the pension fund participant. It is emphasized that, while a simple way of covering oneself against the option price variations would be neutralizing their effects, via a delta neutral cover for example, the principle of optimality requires solving for the optimal portfolio rules. It is proved that the existence of a guarantee leads to the emergence, in the optimal investment policy rule, of an additional preference independent guarantee hedge term, whose formulation depends on the characteristics of the analyzed guarantee.
Keywords: Pension funds, Options, Asian exchange option, Monte Carlo simulation, Optimal portfolio, Hedging
JEL Classification: G23, G13, G11, C61
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