THE PRICING OF FORWARD-STARTING ASIAN OPTIONS

Asian options are path-dependent options whose payoff is based on an average. In some cases, the underlying asset of the option is an average; in others, the strike price itself is computed as an average of the underlying asset recent prices. Asian currency options, as an example, allow corporate users to cover seasonal and so-called strategic foreign exchange positions. Averages are also found in some recent warrant issues, where they are mostly used as poison pills to preclude hostile takeovers. This paper derives a closed-form solution for the valuation of European asian options whose strike price is an average. Both ''plain vanilla'' average options-i.e. those for which the time interval taken into account for the strike average calculation is the life of the option-and forward-starting average options are considered. The valuation formula is obtained by relying upon a slight linear approximation. Although some previous contributions in the literature already use approximation techniques, our approach contrary to others allows the derivation of a formal upper bound to the approximation error. The numerical values given by this formula are then compared to those generated by an antithetic variate Monte-Carlo method. Based on this comparison and the computation of an upper bound to the approximation error, it is shown that the closed-form solution performs quite well and is obviously computationally efficient.