Implied volatility

[JackieJin]

Just read a post
http://www.theoptionsguide.com/volatility-smile.aspx.

And came up with three statements below. Can anyone judge if those are correct? If not, how do we tell if the B-S overestimates market price or underestimates market price?

1. In the reverse skew implied volatility scenario, Deep OTM put and deep ITM call are more expensive in the market than from the B-S. Deep OTM call and deep ITM put are less expensive in the market than from the B-S.

2. In the forward skew implied volatility scenario, Deep OTM call and deep ITM put are more expensive in the market than from the B-S. Deep OTM put and deep ITM call are less expensive in the market than from the B-S.

3. In the smile scenario, deep OTM and deep ITM options are more expensive in the market than from B-S.

 

[rajanS]

Just read a post
http://www.theoptionsguide.com/volatility-smile.aspx.

And came up with three statements below. Can anyone judge if those are correct? If not, how do we tell if the B-S overestimates market price or underestimates market price?

1. In the reverse skew implied volatility scenario, Deep OTM put and deep ITM call are more expensive in the market than from the B-S. Deep OTM call and deep ITM put are less expensive in the market than from the B-S.

2. In the forward skew implied volatility scenario, Deep OTM call and deep ITM put are more expensive in the market than from the B-S. Deep OTM put and deep ITM call are less expensive in the market than from the B-S.

3. In the smile scenario, deep OTM and deep ITM options are more expensive in the market than from B-S.

I didn't read the link you posted but from my reading on options markets over the years...I have picked up the following ideas...
its not perse that a skew means more or less expensive than the B-S. When you pass different strikes obtained from the market (question: where do you get the strikes, how many strikes do you get? how do you interpolate between strikes?), you end up getting different imp vol associated with those strikes. There is a whole line of thought that skew comes from stochastic volatility models. Hence, to determine if market is under pricing or over pricing, you have to look at whether they are using local or stochastic vol models.

your line of thought should be:
in equity market, it exhibits negative skew. Hence, deep ITM calls and OTM puts are more expensive. OTM puts are more expensive because in the downside, ppl find it cheaper to buy OTM puts, hence they bid their prices up. Only way black scholes accounts for higher prices, is by spitting out higher imp vol. Another reason by OTM puts are more expensive, is when stock price falls, OTM puts become more ITM and their gamma increases. As gamma increases, option becomes more expensive to hedge and risky. Only way option market makers(who have short position in the OTM puts) would undertake such a position is if they were offered a higher price. Hence, OTM puts are more expensive. Can you think of why deep ITM calls are more expensive?

It gets more advanced that this. You can also think of a skew as being bounded by prices of call and put spreads. Hence, we can think of skew in terms of prices of digitals.