Implied Distriubtion

[Liming]

Dear David,

I have some confusion over the illustration of "Smile Effect" of implied distribution on page 354 of FRM handbook(5th edition). Figure 14.6 graphically plots the relationship between volatility (%) and the ratio of current spot price to strike price for a put option and show that it looks like a smirk because the implied volatility is higher for out-of-money put than at-the-money put.
I don't understand why the ratio corresponding to out-of-money put is less than 1. With the ratio less than 1, or current spot price less than strike price, I think the put option should be In-The-Money not out-of-money. Therefore figure 14.8 should plots the smirk in an opposite direction.
Thank you for correcting me!

Cheers
Liming
18.10.09

 

[David Harper CFA FRM]

Hi Liming,

I agree, it's wrong (good observation)!.

The graphic (without labels) does show the familiar "volatility smirk", but as you suggest, the X-axis should be "Strike Price" or (without loss of meaning) ratio of Strike/Stock
...further the text does not seem to distinguish between a put and a call, so the text *appears* doubly wrong to me (at first glance)
...if you consider the equity smile, see here: http://forum.bionicturtle.com/viewthread/1673/

Per John Hull Figure 18.3.
Higher strike implies lower volatility, in which case:

1. deep out of money put and deep in the money call (i.e., left side of chart, where X axis is strike or strike/spot) have higher volatility and
2. deep in the money put and deep out of money call (right hand side) have lower volatility and

(Hull, 7th, page 394)

Thanks, David