Portfolio Optimization Using SPEA2 with Resampling

Proceeding of: Intelligent Data Engineering and Automated Learning – IDEAL 2011: 12th International Conference, Norwich, UK, September 7-9, 2011The subject of financial portfolio optimization under real-world constraints is a difficult problem that can be tackled using multiobjective evolutionary algorithms. One of the most problematic issues is the dependence of the results on the estimates for a set of parameters, that is, the robustness of solutions. These estimates are often inaccurate and this may result on solutions that, in theory, offered an appropriate risk/return balance and, in practice, resulted being very poor. In this paper we suggest that using a resampling mechanism may filter out the most unstable. We test this idea on real data using SPEA2 as optimization algorithm and the results show that the use of resampling increases significantly the reliability of the resulting portfolios.The authors acknowledge financial support granted by the Spanish Ministry of Science under contract TIN2008-06491-C04-03 (MSTAR) and Comunidad de Madrid (CCG10- UC3M/TIC-5029).Publicad

Estimation of risk-neutral density surfaces

Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness for the estimation and an optimization model to choose the spline functions that best fit the price data. Semidefinite programming is employed to guarantee the nonnegativity of the densities. We illustrate the process using synthetic option price data generated using log-normal and absolute diffusion processes as well as actual price data for options on the S&P500 index. We also used the risk-neutral densities that we computed to price exotic options and observed that this approach generates prices that closely approximate the market prices of these options