PRICING AN INSURANCE AGAINST INVESTMENT YIELD DEVIATIONS FOR ARGENTINE PENSION FUNDS BY A Q.pdf

PRICING AN INSURANCE AGAINST INVESTMENT YIELD DEVIATIONS FOR ARGENTINE PENSION FUNDS BY A QUASI MONTE CARLO METHOD Mariano Cane? de Estrada Superintendencia de AFJPs Tucuma?n 500, (1049) Buenos Aires, Argentina. e-mail: mcane@.ar and Elsa Cortina ? Instituto Argentino de Matema?tica (CONICET), Saavedra 15, 3er. piso, (1083) Buenos Aires, Argentina e-mail: elsa iam@.ar JEL classification code: G13, G18, G23 Keywords: insurance, pension funds, call spread, Quasi Monte-Carlo. Abstract In this paper a Quasi Monte-Carlo method, based on Halton sequences, is used to price an insurance on profit deviations for the Argentine pension funds. The insurance is replicated as a 3D European call spread type option, and the problem of pricing this option is solved in continuous time. ?This author is Fellow of the Consejo Nacional de Investigaciones Cient??ficas y Te?cnicas. 1 1 Introduction The pension funds (PFs), managed by private firms called Administradoras de Fon- dos de Jubilaciones y Pensiones (AFJPs), were created in Argentina, in 1994, by the Law 24.241, which is the main legal frame that, although recent modifications, still regulates their activities. To protect the affiliates from excessive volatility and dispersion in returns among the PFs, there are minimum return requirements relative to the weighted average performance of all PFs over a twelve months period. If the return of a PF is less than 70% of the weighted average or if it is lower than the weighted average minus two percentage points, whichever results in a greatest shortfall, the AFJP managing that fund is required to make up for the difference. The AFJPs do this by transferring cash and other assets from a reserve fund of their property to the PFs. In November 2001, Argentina’s National Administration issued a new a regulation modifying the law, namely the decree Nr. 1495/01. As a result, the AFJPs will be allowed, starting during the first half of 2002, the possibility of partially or totally constitute t