Volatilities and Term structures

[ckyeh]

Dear David:

On your webinar 「2010-5-a-Market-Risk」 page 13:
Volatility term structure is relationship between volatility and maturity.
–Tends to be an increasing function for a call option(volatility increases with a longer maturity)

Compared to John Hull’s book Option Futures And Other Derivatives, page 399:
Volatility tends to be an increasing function of maturity when short-dated volatilities are historically low. This is because there is then an expectation that volatilities will increase. Similarly, volatilities tends to be an decreasing function of maturity when short-dated volatilities are historically high. This is because there is an expectation that volatilities will decrease.

Why do you say 「Tends to be an increasing function for a call option」? According to John Hull, Increasing function or decreasing function are all possible. Is it because you specifically mentioned 「a call option」?

Thanks for your help!

 

[David Harper CFA FRM]

Hi chyeh,

It's my mistake, apologies my MISTAKE, it really should not say that. As the graph on the same page (the questions marks, ?) mean to imply (and the graph on page 5), I should not make a general unconditional claim like that. It should make no empirical, unconditional claim.

Alternatively, of course, Hull's point above "mean reversion" can be made as a conditional statement (i.e., if short-term implied vol is low compared the long-run expectation, then we can expect increasing function. But this can go either way, too, so there is nothing unconditionally upward-slopping about the term structure).

Thanks for a careful read (It doesn't help currently, but I make a careful note to not repeat the error).

I hope your studies are going well, based on your careful attention to detail, it certainly seems like you are top of your study schedule!

David