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Derivatives - volatility skew and volatility smile

Hello,

I’m having some trouble with understanding the volatility skew and smile.

1. Volatility smile: volatility is higher for ITM and OTM, compared to ATM. Is that because of the possible gains (ITM) and losses (OTM)?

2. Skew: “to overpay for downside striked options on stocks. This meant that people were assigning relatively more volatility to the downside than to the upside, a possible indicator that downside protection was more valuable than upside speculation in the options market.”

why is that? why is there more volatility to the downside? And what is a “downside strike”?

thanks a lot!

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CaliforniaDreaming wrote:

Hello,

I’m having some trouble with understanding the volatility skew and smile.

1. Volatility smile: volatility is higher for ITM and OTM, compared to ATM. Is that because of the possible gains (ITM) and losses (OTM)?- Yes. But you need to understand it deeper. We are essentially talking about Gains for Put options at  deep (OTM for Call Options) in the money for lower price and Losses  at deep (ITM for Call Options) out of the money at higher price.

2. Skew: “to overpay for downside striked options on stocks. This meant that people were assigning relatively more volatility to the downside than to the upside, a possible indicator that downside protection was more valuable than upside speculation in the options market.”- Yes. you are correct. Think of it more from the Volatlity’s smirk rather than smile.You will loosely find a connection to this in the Behavioral Finance. The pessimist weighs in more than the optimist.

why is that? why is there more volatility to the downside? And what is a “downside strike”?- Downside strike- European call option with a low strike

thanks a lot!- Anytime. But I reckon there will be more questions on your mind regarding this. Go on.

back against the wall. no retreat no surrender.

What you have to understand is that when they’re talking about volatility, they’re really not talking about volatility.  They’re talking about price.

Volatility skew simply means that lower strike options are overpriced, and the lower the strike, the more overpriced they are.  Volatility smile simply means that low-strike options are overpriced, and high-strike options are overpriced.

Remember that the actual volatility is the volatility of the underlying’s returns.  That volatility doesn’t depend on the strike price of options; it is whatever it is.  Properly, all options on a given underlying with the same maturity will have the same implied volatility if the options are fairly priced.

Simplify the complicated side; don't complify the simplicated side.

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Thank you Magician & Herb, I guess you are the masters of these forums…

Magician is definitely the master. I am just a rookie, trying to do my bit and if it may help you and others.

On the topic…the concept is definitely intricate and CFAI does a mediocre job of explaining Volt. Smile and smirk. FRM provides deeper and wider perspective to the whole thing. It is relevant more, I guess there.

For your understanding I will stretch a little more:

1. Volatility smile is more relevant to Fx. For equity options it is Volatility smirk that happens and not smile.

2. Is it theoritical or practical - it is theoritical and not actual .

3. What exactly it is  ? -  Remember BSM and Log Normal Diffusion . Remember Put Call Parity . Now here is the paradox. Put Call Parity is reality as violation of the equality will lead to arbitrage profit. Put Call Parity will hold regardless of how you obtained the European options price. That is to say, that Put Call Parity will hold if the Call and Put options are theoritically gleaned from a model such as BSM. It will also hold from the observed market value of Put and Call. For the same time to expiry and the underlying’s strike price, if we set the equations and simply deduct one eqn. From the another what we get is the difference of the model Call price and actual Call price = difference between the model Put price and actual Put price. If we do this sufficient no. of times for different strike price ( obviously different call and out price and different times to maturity and different Rf- but all of them must necessarily be European type options only), we will get set of such call price differences = put price differences. Now what are these differences - volatility of course .

The above suggests that from the least point of difference ( there will be one set of price difference which will be the least value), the differences grow either way for a call and out option SYMMETRICALLY.

4. Now this is a peaceful solution for all of us because it is theoritically stable. We sure can do a lot of predictions ( like probability of default) with this. The problem comes else where. 

5. Any call option from a lower strike price and any put option from a higher strike price would be more valuable for us. However, the lower strike call option has BIG SHADE of grey. If the equity price is low- it surely puts a lot of pressure on th capital structure of the company as the leverage indirectly increases. An increased leverage raises the probability ( and thus the volatility) of default  as well. Further , Rubenstein studied through the market crash of 1987 and predicted his own default model which is popularly known as ‘Crashophobia’. Crashopobhia also talks about tb possibility of market crash leading to a default. You may further notice that this pessimism is further heightened by human behaviour as well. We as intellectual creature attach more probability to failure than to success as a crowd this depressing further. ( Prospect theory or some bull **** in the behavioral finance section )

6. Now what effect does this have on our European options ? - simple Your lower striked call option even though may be valuable because of low price the volatility here is NOW NOT A FRIEND of this options price because of the market sentiment. While the put option becomes simpler to price because the levrwge problem, crashophobia problem and the pessimism are absent there . The bottom line is the call option now shows more volatility than the put options 

7. When you plot them ( the implied volatility in the Y Axis and the call option price ( reflected as the strike price ) , what you will now notice is not a symmetrical smile but a smirk.

Hope you like it !

back against the wall. no retreat no surrender.

BTW, the smirk is also called the skew, volatility skew.

back against the wall. no retreat no surrender.

wow, yes.. thank you for taking the time!