Mastering Derivatives: Does implied volatility signal future volatility?

Volatility is the most important of the five factors that drive option prices. This week, we discuss why implied volatility is not necessarily a good estimate of realised volatility of an underlying asset.

Time-varying volatility

An option valuation model assumes that returns on an underlying have no autocorrelation. That is, today’s returns on an asset are independent of yesterday’s returns. This assumption makes for easy computation of returns-volatility. You first calculate the one-day returns-volatility of an underlying. Next, you apply the scaling property of volatility. Suppose you want to value an option that has 10 days to expiry, you must calculate the 10-day returns-volatility of the underlying. This is because the option you want to buy ought to price in the expected volatility of the underlying over the remaining 10 days.

The 10-day returns-volatility is determined as one-day returns-volatility times square-root of 10. Why? Variance is proportional to time. That is, two-year returns-variance is double that of one-day returns-variance of an underlying. Standard deviation, the metric for determining volatility, is the square-root of variance.

In real-world markets, volatility tends to cluster. That is, large changes in volatility are likely to be followed by more such large changes. Likewise, small changes in volatility are likely to be followed by more such small changes. This has prompted researchers to forecast volatility using Generalised Auto-regressive Conditional Heteroscedastic or GARCH models. Given the complexity in using these models, option traders tend to use implied volatility. This is derived from the option price for a strike with other inputs being spot price, strike price, time to expiry and risk-free rate.

The implied volatility of the next-week 18600 Nifty call is 13.22. It is tempting to interpret this number as the market’s expectation of the returns-volatility of the Nifty Index over the life of the option. However, implied volatility is not an accurate (unbiased) estimate of the realised (actual) volatility of an underlying asset. This is because returns-volatility of an underlying changes with time. The option on the asset is exposed to such changes in returns-volatility. Therefore, an option ought to price in the risk premium associated with changes in volatility. This is one reason why implied volatility of options for the same strike vary across time. For instance, 18600 Nifty December call trades at an implied volatility of 13.37 per cent compared to 13.22 per cent for the next-week expiry 18600 call.

Volatile times

Large changes in volatility are likely to be followed by more such large changes

Optional reading

If volatility risk premium explains for time-varying volatility, what can account for differences in implied volatility across strikes with same expiry? The valuation model assumes returns are normally distributed. But asset prices exhibit extreme price movements in real-world markets, more frequently than can be explained by normal distribution. Option traders are, therefore, willing to buy out-of-the-money options to gain from such extreme price movements. Varying demand for such options lead to difference in how each strike reacts to an underlying’s price changes, resulting in differing implied volatilities across strikes.

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