sitcky strike rule

[wufuheng1979]

In handbook P409, it says sticky strike is "the curve does not change", but why "the ISD drops from 18 to 17.5" as the strike is still 100???

 

[David Harper CFA FRM]

hi wufu,

that figure 17.4 is arguably confusing. The handbook is trying to illustrate a scenario where the stock price shifts from $100 to $110, and the issue is, what happens to the ISD of an option with a strike (K) of $110?

• under sticky moneyness, as S increases from 100 to 110, an option with K = $110 moves from OTM to ATM, and its implied volatility "remains" at 18% because ATM options previously has ISD = 18%
• under sticky strike, as S increases from 100 to 100, option with K = 110 moves from OTM to ATM, but its implied volatility "drops" from 18% (when it was OTM) to 17.6% (when it is now ATM)

 

[Tipo]

hi wufu,

that figure 17.4 is arguably confusing. The handbook is trying to illustrate a scenario where the stock price shifts from $100 to $110, and the issue is, what happens to the ISD of an option with a strike (K) of $110?

• under sticky moneyness, as S increases from 100 to 110, an option with K = $110 moves from OTM to ATM, and its implied volatility "remains" at 18% because ATM options previously has ISD = 18%
• under sticky strike, as S increases from 100 to 100, option with K = 110 moves from OTM to ATM, but its implied volatility "drops" from 18% (when it was OTM) to 17.6% (when it is now ATM)

Im abit confused and i dont have the text but this is taken from BT notes pg 13 R41.P2.T5.Hull_Ch19_v5

• Sticky Strike rule: implied volatility of an option remains constant from one day to the next
• Sticky Delta rule: relationship between an option price and the ratio stock-to-strike (S/K) is constant

From what i understand, sticky delta=sticky moneyness
How does this tally with the example given in your post?

Thanks!

 

[David Harper CFA FRM]

Hi @Tipo

My post above may be confusing (or even wrong) as I was trying to interpret the FRM handbook explanation (on page 410), but yes, I agree with you that "sticky delta" = "sticky moneyness"

Here is how I look at this: assume today's spot price is $100, S(0) = $100 and the implied volatility of an ATM option, K = 100, is 20.0%. Now imagine that tomorrow the stock price jumps to $110:

1. What is the implied volatility of an option struck tomorrow at K = 100; i.e., ATM?

• If it is unchanged at 20.0%, then sticky money (aka, sticky delta) applies because the implied vol of 20.0% was "sticky" to the money-ness which remains zero; but this requires that the curve shift to the right (consistent with shift in FRM Handbook Figure 17.4)
• If it reduces to something lower, although tomorrow this option will still be ATM (ie, S = 110, K = 100), then sticky strike rule is implied and the implied vol curve--because its axis is the strike price not the asset price--did not shift.

2. And we can ask what happens to today's option which still has a strike price of 100 (ignoring that the maturity shortened by a day). This option has shifted from ATM to a ITM call or OTM put (by $10)

• if this ITM call/OTM put retains its implied vol of 20.0%, then sticky strike applies: this option is now $10 ITM or OTM but the curve did not shift (and it represents a point on the curve which is not longer the local minimum!). In this case, this option's moneyness changed but it's implied volatility did not, so it's NOT stick money.
  
• If this ITM call/OTM put sees an increase in its implied vol (assuming a typical equity skew), then this must be sticky moneyness: the curve shifted such that, given the same $100 strike (x axis) the corresponding implied vol is higher. Put another way, this is sticky money: the option shifted from ATM to in or out of the money (money changed), so implied vol changed.