Estimating Changing Volatility in Cash Flow Simulation Based Real Option Valuation with Regression Sum of Squares Error Method

This paper presents a practical volatility estimation method for cash flow simulation based real option valuation with changing volatility. During cash flow simulation, present value of the future cash flows and their corresponding cash flow state variable values are recorded for all time periods. Then, for each time period, regression analysis is used for relating the present value to the cash flow state variables of the same time period. Each regression equation provides an estimate of the expected present value as a function conditioned on the resolution of all uncertainties up to that time. Then, basic regression statistics of Pearson's correlation R2 and sum of squares error (or standard error) for each equation provide all the information required for estimating how the standard deviation and volatility of the stochastic process change over time. The method is computationally efficient because it requires only one pass of simulation runs regardless of the number of time periods. It can also handle negative underlying asset values. Straightforward calculation of required regression statistics and their availability in any statistical software and even in spreadsheet programs make this approach very easy to apply for a practitioner