Financial Engineering

The authors propose a likelihood-ratio test of the hypothesis that the minimum-variance frontier of a set of K assets coincides with the frontier of this set and another set of N assets. They study the relation between this hypothesis, exact arbitrage pricing, and mutual fund separation. The exact distribution of the test statistic is available. The authors test the hypothesis that the frontier spanned by three size-sorted stock portfolios is the same as the frontier spanned by thirty-three size-sorted stock portfolios.

A new variable rate refining subdivision B4 for the solution of equations with piecewise linear homotopies and restart homotopies is described. The essential virtue of the subdivision B4 is that it offers vast latitude to the user. In particular, the parameters of B4 can be set so one restriction of B4 is that J3 triangulation and another restriction is the octahedral subdivision. More generally, full flexibility is available in the placement of local focal points, and perhaps most importantly, B4 permits the new capability of refining coordinates at variable and independent rates.

The perturbation generation rule of Suri (Ref. 1) is extended to cases where random variables are not generated by inversion. Conditions are given for the use of other methods. Infinitesimal perturbation analysis is shown to be compatible with common random number techniques in cases where finite-difference approximations are not.

Rational restrictions are derived for the values of American options on futures contracts. For these options, the optimal policy, in general, involves premature exercise. A model is developed for valuing options on futures contracts in a constant interest rate setting. Despite the fact that premature exercise may be optimal, the value of this American feature appears to be small and a European formula due to Black serves as a useful approximation. Finally, a model is developed to value these options in a world with stochastic interest rates.

Let P be a polytope in Rn containing the origin in its interior, and let P* be the algebraic dual polytope of P. Let Q Rn x [0,1] be the (n+1)-dimensional polytope that is the convex hull of P x {1} and P* x {0}.

Improvements in computational methods have resulted in the faster solution of general equilibrium economic models This paper gives a nontechnical introduction to the octahedral algorithm for the solution of economic models.