Chapter 22The Difficult Problem of Estimating Volatility, Mean Reversion, Time Trends, Correlations, and Price Boundaries from Historical Data or Market Data

You may have noticed that none of the discussion in Chapters 20 or 21 explained how to compute parameters necessary to run a simulation such as mean reversion, volatility, or any of the other parameters that are input into time series equations. The exercises in Chapter 21 show the importance of volatility, mean reversion, correlation, and other variables in the risk measurement process, but not what those parameters should be. If the construction of time series equations using parameters of volatility, mean reversion, price boundaries, price jumps, and correlations is to be useful in modeling, you must be able to derive the parameters.

This chapter discusses practical and theoretical issues that arise when attempting to use analysis of past data in computing the various parameters required for a time series equation. In discussing how to compute the various parameters, this chapter explains how to test whether the parameters that are input produce consistent and expected output results as well as mechanical computation of statistics from historical data. To illustrate the importance of testing input parameters relative to output results, assume that a volatility of 20 percent is computed from monthly historical data. But also assume that there is a high degree of mean reversion that is modeled as part of the process. Because ...

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