Optimizing a Portfolio of Equities, Equity Futures and Equity European Options
by Minimizing Value-at-Risk - A Simulated Annealing Framework
Student Name: Ajay Raina
Value-at-Risk, defined as a given quantile of a portfolio
of loss, was minimized to obtain optimal allocation of a unit capital into
different elements of the portfolio. The considered portfolio included
equities, equity futures, and European options on the equities, which made the
return and thus loss non-linear, requiring numerical techniques for
optimization. The loss distribution for a given composition of a portfolio
was computed using monte-carlo simulation, while the optimization of this
composition was performed using simulated annealing, with the iterative step
involving generation of random vectors from a Dirichlet distribution with a
mean at the current step and variance controlled by another parameter
determined by near-optimality of the solution.