# Illustrative Example: Volatility – Volatility Computations

File Name: Volatility – Volatility Computations

Location: Modeling Toolkit | Volatility | Volatility Computations

Brief Description: This model uses Risk Simulator to apply Monte Carlo simulation in order to compute a project’s volatility measure

Requirements: Modeling Toolkit, Risk Simulator

There are several ways to estimate the volatility used in the option models. The most common and valid approaches are:

Logarithmic Cash Flow Returns Approach or Logarithmic Stock Price Returns Approach: This method is used mainly for computing the volatility of liquid and tradable assets such as stocks in financial options; however, it is sometimes used for other traded assets such as the price of oil and price of electricity. The drawback is that discounted cash flow models with only a few cash flows will generally overstate the volatility and this method cannot be used when negative cash flows occur. This means that this volatility approach is only applicable for financial instruments and not for real options analysis. The benefits include its computational ease, transparency, and modeling flexibility of the method. In addition, no simulation is required to obtain a volatility estimate. The approach is simply to take the annualized standard deviation of the logarithmic relative returns of the time-series data as the proxy for volatility. The Modeling Toolkit function MTVolatility is used to compute this volatility, where the time series of stock prices is arranged in time series (can be chronological or reverse chronological). See the Log Cash Flow Returns example model under the Volatility section of Modeling Toolkit for details.

Exponentially Weighted Moving Average (EWMA) Models: This approach is similar to the previous logarithmic cash flow returns approach, using the MTVolatility function, to compute the annualized standard deviation of the natural logarithms of relative stock returns. The difference here is that the most recent value will have a higher weight than values farther in the past. A lambda or weight variable is required (typically, industry standards set this at 0.94), where the most recent volatility is weighted at this lambda value, and the period before that is (1 – lambda), and so forth. See the EWMA example model under the Volatility section of Modeling Toolkit for details.

Logarithmic Present Value Returns Approach: This approach is used mainly when computing the volatility of assets with cash flows. A typical application is in real options. The drawback of this method is that simulation is required to obtain a single volatility and is not applicable for highly traded liquid assets such as stock prices. The benefits include the ability to accommodate certain negative cash flows and to apply more rigorous analysis than the logarithmic cash flow returns approach, providing a more accurate and conservative estimate of volatility when assets are analyzed. In addition, within, say, a cash flow model, multiple simulation assumptions can be set up (we can insert any types of risks and uncertainties such as related assumptions, correlated distributions and nonrelated inputs, multiple stochastic processes, and so forth), and we allow the model to distill all the interacting risks and uncertainties in these simulated assumptions and obtain the single value volatility, which represents the integrated risk of the project. See the Log Asset Returns example model under the Volatility section of Modeling Toolkit for details.

Management Assumptions and Guesses: This approach is used for both financial options and real options. The drawbacks are that the volatility estimates are very unreliable and are only subjective best guesses. The benefit of this approach is its simplicity––this method is very easy to explain to management the concept of volatility, both in execution and interpretation. That is, most people understand what probability is, but have a hard time understanding what volatility is. Using this approach, we can impute one from the other. See the Probability to Volatility example model under the Volatility section of Modeling Toolkit for details.

Generalized Autoregressive Conditional Heteroskedasticity (GARCH) Models: These models are used mainly for computing the volatility of liquid and tradable assets such as stocks in financial options. They are sometimes used for other traded assets such as price of oil and price of electricity. The drawbacks are that a lot of data is required, advanced econometric modeling expertise is required, and this approach is highly susceptible to user manipulation. The benefit is that rigorous statistical analysis is performed to find the best-fitting volatility curve, providing different volatility estimates over time. The EWMA model is a simple weighting model whereas the GARCH model is a more advanced analytical and econometric model that requires advanced algorithms such as the generalized method of moments to obtain the volatilities.

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