Market Risk question 3.6 on implied vol. smile

[pmf0770]

Question 3.6. is as following: "Option writers (market makers who take short positions) are averse to high delta call options but prefer low delta call options?"

You wrote: "Because supply is lower for OTM call options (delta nearer to zero!) and supply is higher for ITM call options (delta nearer to 1.0), ..."



I thought it is the opposite. If writers are averse to high delta call options, the supply to high delta call options must be lower. Since high delta call options are ITM call options, the price for ITM call options must be higher, implying a higher volatility where strike is low.



Would you please comment? Thx.



 

[David Harper CFA FRM]

Hi pmf,

Yes, I agree! I think i got it exactly wrong, looks like it should be (as you suggest):

Replace:
03.06. Option writers (market makers who take short positions) are averse to high delta call options but prefer low delta call options?
Because supply is lower for OTM call options (delta nearer to zero!) and supply is higher for ITM call options (delta nearer to 1.0), this dynamic would promote an inverted skew: lower implied volatility on the left tail and higher implied volatility on the right tail. That is, on the right (higher strike price), OTM call options are less supplied so their price is higher so the implied volatility is higher.

With:
03.06. Option writers (market makers who take short positions) are averse to high delta call options but prefer low delta call options?
Because supply is higher for OTM call options (delta nearer to zero!) and supply is lower for ITM call options (delta nearer to 1.0), this dynamic would promote an equites-like skew: higher implied volatility on the left tail and lower implied volatility on the right tail. That is, on the right (higher strike price), OTM call options in greater supply (being preferred for their lower delta) so their price is lower (increase supply --> lower price) so the implied volatility is lower.

Apologies (this is tricky), really excellent catch on your part, thank you for the correction!

corrected with credit @ http://forum.bionicturtle.com/threads/l2-t5-03-shape-of-implied-volatility-smile.3375/

 

[Mark W]

Yep, and further typo:

That is, on the right (higher strike price), OTM call options in greater supply (being preferred for their lower delta) so their price is lower (increase supply --> lower price) so the implied volatility is lower.