Volatility Skew


If we try to compute the volatility of an underlying by feeding in the required variables and the market prices of the options into the Black Scholes option pricing model, theoretically, options with same expiration date should have same implied volatility regardless of the strike prices we input.


But in reality, the implied volatility we get across various strikes is different. This difference in volatilities across its respective strikes is known as volatility skew. When implied volatility is plotted against its respective strike price, the resulting graph can be a U-shaped or downward sloping.


Volatility Smile, Reverse Skew, Forward Skew


If the plotted graph is a U-shaped curve, as shown in Figure 1.1 below, this volatility skew pattern is also referred to as a volatility smile as it resembles a smile.


The U-shaped volatility smile skew pattern is common for equity options which are near-term and options in the forex market. Volatility smile indicates that the demand is greater for options that are in-the-money or out-of-the-money.


But, for longer term equity options and index options the reverse skew patterns are typical (Figure 1.2). In the reverse skew pattern, the implied volatility of options at the lower strikes is higher than the implied volatility at higher strikes.


This reverse skew pattern implies that in-the money calls and out-of-the-money puts are more expensive and more in demand as compared to out-of-the-money calls and in-the-money puts.


This pattern can arise in two cases; either, when the investors are worried about market falls, so they hedge their positions by buying puts for protection, or the other explanation can be, that in-the-money calls have become alternatives to outright stock purchases as they offer leverage and hence increased return on investment. In both cases greater demand is created for in-the-money calls and therefore it results in increased implied volatility at the lower strikes.


As against reverse skew, forward skew is another type of the volatility smirk (Fig. 1.3), where, the implied volatility for options at the lower strikes is lower than the implied volatility at higher strikes.

In this case, the out-of-the-money calls and in the-money puts are in greater demand as compared to in-the-money calls and out-of-the money puts. The forward skew pattern is common for options in the commodities market where there can be a supply crunch, business houses would be ready to pay higher prices to secure supply than to risk supply disruption.


Concluding, for option traders the best market direction assessment and option price evaluations can only be drawn by inter comparison of implied volatility with historical, current and forecasted volatilities, by assessing if they are over or under priced.


This is the Volatility Smile of Nifty as on at the market closing of 11th June 2010. As mentioned above it is a typical long term index option, with the reverse skew pattern.


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One response to this post.

  1. Posted by automated forex trading on June 29, 2010 at 8:31 AM

    Nice blog,i’ll bookmark your blog for the future.
    Thank you very much and keep sharing


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