Recommendations: 2
kit...
here's a simple explanation of sticky deltas and volatility smiles... http://www.riskglossary.com/link/volatility_skew.htm
the idea of a sticky delta is pretty easy to conceptualize. As in the example... assume an option exibits a delta of .5 when the instrument is priced at 75 and the strike is 75...
then if the instrument moves to 80, a "sticky delta" would imply that an option with an 80 strike should now have a delta of .5
the delta is "sticky" and keeps it relation with successive at the money strikes.
my understanding is that assuming a sticky delta allows predictive modeling of option prices in a way that more typical models do not achieve ......................................
the volatility smiles and skews are interesting and pretty intuitive. Simply graph the calculated volatilities of a series of strikes and connect the dots. You get a characteristic curve. It may be a smile, a skew, a "smirk" or what ever. I think the idea is that the shape of the curve of volatilities generally remain constant for a particular asset. If that's true then there is a predictive ability in forcasting volatilities of various strikes in relation to changes in the underlying asset. For instance, calculate the volatility for MMM Jan06 $85 call when MMM sells at 70. If MMM moves to 80, you should be able to make a prediction on how the Jan06 $95 call should be priced via use of the graph of volatilities.
(anyone... please feel free to correct me) ................................................................. Also I use a spreadsheet for valuing options and there is no input for varying the input for different percentages for upside and downside risk. How would you do this? Calculations by hand are not an option :)
The binominal option pricing model Naj suggested would do it but for one big problem... binominal pricing models use a recursive pricing procedure that is based on the assumption of risk neutrality and constant volatility. (the mentional trinominal model can handle changes in volatility but I don't have any idea how trinominal trees work) There are bunches of excel addin's that apply binominal pricing models. I started a series of posts a while back on options and implied volatilities that I never really finished. It seemed to me that all equity option pricing models require an assumption of an efficiently priced equity. If an equity is inefficiently priced, that should translate into the option prices... but I don't find that anywhere. I thought the sticky delta idea might lead somewhere... but Naj is exactly right, a simple binominal pricing model would do the trick if one were able to make one very small alteration. I hope someone reads this.... what would happen to an option pricing model on MMM if you assumed the equity simply would not fall below 60 during the life of the option
that would have exactly the effect I was thinking about... the closer you get to 60, the more compressed "true" put values would be. If you assume MMM cannot go below 60, then any put below 60 would have a negative value regardless of price and should be sold. Likewise, the closer you get to 60, the greater the "true" value of a call option would be.
what's magic about 60? nothing... but make these assumptions... MMM really truly is worth $90 per share, $60 purchase really truly does give one a 50% margin of safety... and making those assumtions plus the idea that the swtock cannot fall below any specified number with/in the option period indroduces the idea of inefficient equity pricing into the option equation
I need the coven of quants to develop an option pricing model that includes inputs for the intrinsic value of the underlying asset, a margin of safety of the underlying, and a floor through which the asset is "highly unlikely" to fall.... then you'd have an option pricing model for the value investor
it's late... I'm on call and we've now had 16 new admissions from south Miss and my Coup de GrĂ¢ce... the 500lb acute resp failure who floated out of the big easy
lordy



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