On the non-linear relationship between VIX and realized SP500 volatility

Buy and hold strategies make staying disciplined difficult for investors, especially given the variability of returns for different asset classes/strategies during divergent market conditions. Market timing strategies, on the other hand, present significant theoretical benefits, but in reality these benefits are difficult to obtain. Tactical asset allocation, where limited deviations from the strategic allocation are allowed permits the portfolio manager to take advantage of market conditions fits between these two extremes. The authors correlate daily returns for each of eighteen separate asset classes typically used in diversified institutional portfolios and daily closing values of the VIX (the ticker symbol for the Chicago Board Options Exchange Volatility Index). This information is used to select those classes whose returns are most responsive to the level of the VIX. Portfolio allocations for eight selected asset classes are revised depending on the level of the VIX at the daily close of the market. The portfolio is rebalanced on the business day following the day the VIX hits the trigger value. The VIX tactical allocation overlay yields an increase in return over the buy and hold portfolio of approximately 38 basis points. The authors conclude that the tactical asset allocation strategy based on the level of VIX provides a higher return than the neutral buy and hold allocation with a higher Sharpe ratio and lower volatility.

The asset management sector is constantly looking for a reliable investment strategy, which is able to keep its promises. One of the most used approaches is the target volatility strategy that combines a risky asset with a risk-free trying to maintain the portfolio volatility constant over time. Several analyses highlight that such target is fulfilled on average, but in periods of crisis, the portfolio still suffers market’s turmoils. In this paper, the authors introduce an innovative target volatility strategy: the discontinuous target volatility. Such approach turns out to be more conservative in high volatility periods. Moreover, the authors compare the adoption of the VIX Index as a risk measure instead of the classical standard deviation and show whether the former is better than the latter. In the last section, the authors also extend the analysis to remove the risk-free assumption and to include the correlation structure between two risky assets. Empirical results on a wide time span show the capability of the new proposed strategy to enhance the portfolio performance in terms of standard measures and according to stochastic dominance theory.

The problem of calibration of local volatility model of Dupire has been formalized. It uses genetic algorithm as alternative to regularization approach with further application of gradient descent algorithm. Components that solve Dupire’s partial differential equation that represents dynamics of underlying asset’s price within Dupire model have been built. This price depends in particular on values of volatility parameters. Local volatility is parametrized in two dimensions (by Dupire model): time to maturity of the option and strike price (execution price). On maturity axis linear interpolation is used while on strike axis we use B-Splines. Genetic operators of mutation and selection are then applied to parameters of B-Splines. Resulting parameters allow us to obtain the values of local volatility both in knot points and intermediate points using interpolation techniques. Then we solve Dupire equation and calculate model values of option prices. To calculate cost function we simulate market values of option prices using classic Black-Scholes model. An experimental research to compare simulated market volatility and volatility obtained by means of calibration of Dupire model has been conducted. The goal is to estimate the precision of the approach and its usability in practice. To estimate the precision of obtained results we use a measure based on average deviation of modeled local volatility from values used to simulate market prices of the options. The research has shown that the approach to calibration using genetic algorithm of optimization requires some additional manipulations to achieve convergence. In particular it requires non-uniform discretization of the space of model parameters as well as usage of de Boor interpolation. Value 0.07 turns out to be the most efficient mutation parameter. Using this parameter leads to quicker convergence. It has been proved that the algorithm allows precise calibration of local volatility surface from option prices.