More About Volatility Skews, Crunches And Smiles

Regular readers will by now be familiar with the fact that one of the most popular options valuation models out there is the Black-Scholes model.

Black-Scholes uses a number of inputs to calculate a fair market value for a European-style option. One of these inputs is the volatility.

Modern traders, however, often use Black-Scholes in a different way: they already have the price of the option, which is the price quoted by the market maker. They therefore use this price to reverse calculate the implied volatility of the options.

Volatility discrepancies: the volatility smile

If one follows that approach, it seems logical that options with the same expiration date, but different state of ‘moneyness’ would have the same volatility. i.e. ITM, ATM and OTM options for the same expiration date would have the same implied volatility.

In real life this is seldom the case. A well-known example is that of the so-called volatility smile. The principle is illustrated below in Fig. 9.26(e)



What becomes immediately clear is that the chart is not flat, as one would normally expect. Instead implied volatilities for ITM and OTM options are markedly higher than that of ATM options.

What can a trader deduce from this? An option with a volatility smile simply tells the trader that demand for ITM and OTM options are higher than demand for ATM options. This happens very often with near-term stock options and it is also a common phenomenon in the world of forex options.

A volatility smile also usually appears when a stock or currency is particularly volatile, i.e. the possibility of rapid price movements has already been discounted in the price of ITM and OTM options. Everything else being equal, this could present an opportunity for traders who could exploit the situation with volatility strategies such as the long straddle.

The volatility skew
With the volatility skew traders have a different scenario. Here also there is no straight line depicting volatilities for a given expiration date, but in this case it’s only ITM options that exhibit higher volatilities.

In this case volatilities for ATM and OTM options, although not forming a straight line, are closer to the values predicted by the Black Sholes model. An increase in demand for ITM options, however, results in higher than expected volatilities for these options.

Volatility crunch

More beginner traders have probably lost money through the unexpected workings of the volatility crunch than through any other phenomenon in the world of options trading.

The volatility crunch usually strikes just after a major announcement from a company, e.g. an earnings report. Assume e.g. company ABC is expected to announce sterling profits in a few days’ time. The price of call options starts to increase dramatically and on the basis of that trader John decides to buy a few contracts of ABC calls.

After the profit announcement the price of Company ABC shares indeed rocket by perhaps 10% – but when trader John opens his options trading account, he finds to his dismay that the price of his call options had in fact started to drop.

This is the volatility crunch in action. Experienced options traders started buying ABC call options much longer before the time than trader John. When the earnings announcement was finally made, these astute traders had already started selling their call options again. Suddenly there were no buyers for ABC call options; implied volatility collapsed and the price of these options started to plummet.

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