Financial Derivatives Toolbox

Hedging with Constrained Portfolios

Both hedging functions cast the optimization as a constrained linear least squares problem. (See the function lsqlin in the Optimization Toolbox for details.) In particular, lsqlin attempts to minimize the constrained linear least squares problem

where C, A, and Aeq are matrices, and d, b, beq, lb, and ub are vectors. In all cases of interest for the Financial Derivatives Toolbox, x is a vector of asset holdings (contracts).

This section provides some examples of setting constraints and discusses how to recognize situations when the least squares problem is improperly constrained. Depending upon the constraints and the number of assets in the portfolio, a solution to a particular problem may or may not exist. Furthermore, if a solution is found, the solution may not be unique. For a unique solution to exist, the least squares problem must be sufficiently and appropriately constrained.

Portfolio Rebalancing

Example: Fully Hedged Portfolio