Forecast Volatility

When looking at an option calculator for the first time, everything seems fairly straight-forward: OK, I can input the share price ; strike price ; interest rate (well, around, x%, it doesn’t seem to make that much difference); dividend yield (ditto); maturity easy. but, volatility. where do I find that? Unlike the input parameters interest rate or dividends. there is no obvious reference, and, importantly, the option fair value is sensitive to small changes in this volatility figure.

To calculate the fair value, an option model requires the input of volatility, or, more precisely, the input of: forecast volatility of the share price over the period to expiry of the option. The big question (the art ) of option theory is how to estimate this forecast volatility. This single stage provides gainful employment for a legion of academics, analysts and traders. An estimate of future share price fluctuations — plenty of room for wooliness there!

It must be said immediately, that there is no one correct method of determining the volatility input. Every trader works constantly at refining and adapting their option valuation parameters.

The common place to start when estimating volatility input, is to look at the historic volatility of the share price. So, for example, if share price historic volatility over the past 2 years is 23%, this figure may be used as the model’s forecast volatility input (i.e. forecasting that share price volatility will be 23% over the option’s life).

However, as noted above, the historic volatility value will depend greatly on the time period chosen for the calculation. Some might argue that the most appropriate period to look at, for valuing a 3-month option, is just the last 3 months of share prices. Others will calculate historic volatilities for a range of periods and then take some kind of weighted average.

It is always useful to refer to the implied volatility ; but this is of only limited use when estimating a forecast volatility input. One must be careful of a certain element of circularity here (if a fair value of x is given by the input of y, then the input of y gives a fair value of. x. Voila! Er, yes).

Sometimes, the implied volatilities for other options (within the same sector or market) may also be determined and an average used for the calculation for a specific option.

One of the assumptions of the Black-Scholes model is that volatility is constant over the life of the option. This is obviously unrealistic in real-life, and can cause problems, particularly when valuing longer-dated options. Some of the latest research into option theory is looking at this variation in volatility and trying to refine the model accordingly.

Above all, however, the most important factor to take into account when estimating volatility is: what are you going to do with the output calculation. For example, one may calculate an option value of 55, see that the option is actually trading at 45 in the market, and therefore deem it undervalued. Now what? Just because an option is subjectively undervalued doesn’t mean that the price is going to rise. Hence, while one never wants to buy grossly over-priced options, fair value is of limited use when speculating with options — by far the over-riding determining factor will be the performance of the share price. However, if looking at a combination option strategy (or hedging or arbitraging) an option model is more useful, and the forecast volatility may have to be more a relative (against other options) rather than an entirely absolute estimate.