Unconditional return disturbances: A non-parametric simulation approach |
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| Institution: | 1. Hochschule für Bankwirtschaft Sonnemannstraße 9-11, D-60314, Frankfurt am Main, Germany;2. Dipartimento di Teoria Economica e Metodi Quantitativi, University of Rome “La Sapienza”, Piazza Aldo Moro, 5 00185 Roma, Italy;1. Finance and Financial Services, College of Business, Victoria University, Australia;2. School of Economics, Finance and Marketing, RMIT University, Australia;1. Bogazici University, Department of Economics, Natuk Birkan Binasi Kat: 2 Bebek, 34342 Istanbul, Turkey;2. Tilburg University – European Banking Center, Department of Economics, Room K322B, 5000 LE Tilburg, The Netherlands;1. University of Sussex, UK;2. Department of Economics, Lancaster University Management School, UK;3. Department of Economics, State University of New York, Binghamton, USA;4. Bank of Greece, Greece;1. Department of Finance, College of Business, Chung Yuan Christian University, Taiwan;2. Department of Finance, School of Management, National Central University, 300 Jhongda Rd., Jhongli, Taoyuan 32001, Taiwan |
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| Abstract: | 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 either totally non-parametric when constant volatility is assumed; or semi-parametric in presence of GARCH(1, 1) volatility. Without a loss in accuracy, it is shown to be much more powerful in terms of computer efficiency than the Monte Carlo approach. It is also extremely simple to implement and can 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. |
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