Simulation methods are extensively used in Asset Pricing and Risk Management. The most popular of these simulation approaches, the Monte Carlo, requires model selection and parameter estimation. In addition, these approaches can be extremely computer intensive. Historical simulation has been proposed as a non-parametric alternative to Monte Carlo. This approach is limited to the historical data available.
In this paper, we propose an alternative historical simulation approach. Given a historical set of data, we define a set of standardized disturbances and we generate alternative price paths by perturbing the first two moments of the original path or by reshuffling the disturbances. This approach is totally non parametric when constant volatility is assumed, or semi-parametric in presence of GARCH (1,1) volatility and is shown without a loss in accuracy to be much more powerful in terms of computer efficiency than the Monte Carlo approach. This approach is extremely simple to implement and is shown to be an effective tool for the valuation of financial assets.
We apply this approach to simulate pay off values of options on the S&P 500 stock index for the period 1982-2003. To verify that this technique works, the common back-testing approach was used. The estimated values are insignificantly different from the actual S&P 500 options payoff values for the observed period.
This is joint work with Rita L. D'Ecclesia, University of Rome "La Sapienza".