## Volatility Smile – Usage in the Market

**Volatility Smile- Usage in the market**

A geographical pattern of implied volatility that arises while pricing financial options having the same expiration date and different strike prices, is considered as a graph of Volatility Smile. As per the Black Scholes option pricing model, the volatility of underlying stocks can be computed using market prices, hence if the strike prices are plotted against each other and as the options go more In-the-Money (ITM) and Out of the Money (OTM), the skewness of the graph takes up the shape of U-curve, resembling a smile, thus the name being Volatility Smile.

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**What does the Volatility Smile imply?**

The volatility smile was first observed in the aftermath of the stock market crash of Black Monday in 1987. Factors which make up the value of options mainly consist of the time until the expiration date; strike price in relation to the underlying asset; expected volatility of the underlying asset during the life of the option and as per the Black Scholes model, Implied Volatility is one the main determinants in the pricing of options. The volatility smile reflects the pricing of options which is more complex than the pricing of commodities and stocks. A smile in the Volatility curve implies that overall market volatility in a specific stock increases due to extreme price movements which may lead to a rush for Out-of-the-Money options for speculators meanwhile the vice versa happens for investors. It also depicts the nature of stock being more speculative than the stocks displaying a Skew in their Volatility Curve.

**How it is determined?**

Implied Volatility is used as a tool by traders to keep track and balance the demand and supply of options contract. The Volatility Smile cannot be plotted without finding the Implied Volatility of the option at each strike price using the Black Scholes model, thus Implied Volatility plays a key role in determining the extrinsic value meanwhile the price of underlying stock determines the intrinsic value. If a severe event happens, it may trigger a major change in the price of options, which is why the implied volatility needs to be factored in. Apart from the implied volatility of various prices, volatility smiles can also be computed using single stock price charting. A combination of both these methods gives a 3D known as the Volatility Surface, which gives a complete picture of the implied volatility change.

**Volatility Skew/Smirk:**

While Volatility Smile is prominent for near-term equity as well as forex options, a more common pattern is the Reverse Skew or the Volatility Smirk, which is used for long-term equity and Index options. The Smirk in Volatility curve depicts that in-the-money calls and out-the-money puts are more expensive in comparison to out-the-money calls and in-the-money puts.

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**Limitations of Using the Volatility Smile:**

The volatility smile, though, is just a model, and the implied volatility of options does not actually be aligned with it. It’s aligned with a reversed or forward skew rather than a smile. A volatile smile may not always have a clear U-shape. It may arise as a result of external market conditions such as demand and supply disparities. As a result, the trader must take several considerations to make trading decisions.

**Author: Palak Arora**

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