BOUNDS ON CONTINGENT CLAIMS BASED ON SEVERAL ASSETS

In 1987, Lo derived an upper bound on the price of a European call opt ion on a single asset. Lo's bound depends only on the mean and varianc e of the terminal asset price and is termed a semi-parametric bound. T his paper derives similar semi-parametric bounds on a European call on the maximum of any number of assets. A distribution-free bound for th e price of this option is obtained. The bound depends only on the mean s and covariance matrix of the returns on n underlying assets. The bou nd is obtained by optimizing over the entries of a positive definite m atrix A. This can be accomplished by a technique known as semidefinite programming. We demonstrate the methodology using two specific applic ations. The first concerns the valuation of a European call option on the maximum of several assets. This is known as an outperformance opti on and is of some practical interest. The second application concerns the valuation of a discretely adjusted lookback option. These lookback options are of interest in connection with certain equity annuity ins urance products.