Implied vol from American options

[cquand]

Good morning,



My purpose is calibrate a volatility surface for single stocks.



What is the market standard option pricing model generally used to back out implied volatlity from the American option prices on single stocks?

- Dividend treatment: Discrete or continuous or mix div (Discrete for short-term and continuous for longer term: in this case, what is the breakdown of the term structure generally used?)

- Model: whaley, Barone-Adesi, Bjerksund (continous) or non recombing tree (discrete) or smtg else?



Thanks for your help

[Graeme]

Discrete cash divs as far as there are broker forecasts, then discrete percentage divs using some or other model to forecast these percentages.



Then finite difference for finding implied vol. You can do a few tricks to make this faster than what you might think. For example, you can use one of the approximations that you mention to get the solver started and then refine with actual finite difference; or start with large steps (in time and stock) and then refine as you get closer to the solution. A first estimate might be found by assuming the option is European, for example.



Beware: smoothing out discrete dividends into a continuous dividend yield is a potential source of great toxicity.

[cquand]

Thanks for your reply.



Actually, regarding discrete div, I face sometimes a problem re the "call-put parity" (as in the implied vols of the call and put for a same strike are different:

- no dividend are due before expiry, the call put parity is phuked (I obtain joker vol smile!) - Two Divs and Two Expiry: I cannot manage to find a combinaison of div, which would make the smile fine for both of them



Any guess what would be the problem?



Also I heard that the standard appraoch would be to use a discrete div model for the short-term options but one should use a continuous div model for the longer term, as vol is underestimated otherwise. Is that correct?

[pj]

>Also I heard that the

> ...

>Is that correct?

Yes.

[Baltazar]

cp parity only works for european options

plus beware you are not using stale "last traded" prices.



that might explain your problem

[pj]

What Baltazar said.

[cquand]

I did not mean the call put parity as the equality but more the fact if my forward is wrong, I will extract a vol smile which is not continous when I start to use call instaed of put. In this case, it does mean than my forward i.e. my div estimates are wrong, right?

[TakeItAndRun]

Since the cp parity is true phor European options, you get 2 volatility surphaces. Then, you use the semi-surphaces corresponding to OTM options.



Don’t phorget that a volatility surphace relies on a dividend model. As long as one uses the same consistent div model, everything is phine.



One last thing, use market data phor the phorward (div swap, synthetics, or why not assuming pc parity phor the ATM strike).

[cquand]

We have two vol surfaces? one for american and for one for European?



I went to conference and the following methodology was suggested: (I assume here one ex-date before the expiry):



- guess a div amount d1



- back out implied vol for each option using an american pricer disc. div.



- price the european call and put for the same (I guess for the nearest ATM will be sufficient)



- compute the div amount d2 from the put call parity relationship



- iterate until d1 = d2



Does that make sense?

[TakeItAndRun]

Two questions, two answers:

The two surfaces: American calls and American puts. Then, you recover the best part of them.



What I would do (I guess one iteration is sufficient): given a volatility and an initial dividend, the phirst derivative of call (and put) with respect to dividend, what is the shift of dividend so that the cp parity is satisfied? That's the idea.



Edit: phphphfff