intraday implied volatility

[Robertral]

Robert,

Thank you for pointing out the flaws ?????? – I should have made myself more clear. I should have said some in-the-money options trading at a discount. Near expiry??????? As an arb friend from a US bank pointed out to me, on 2 July (49 days expiry) a number of DAX August calls were at a discount!!!!!!!!.

I didn’t mention anything about otm, time value and no vol. I think intrinsic value and otm are mutually exclusive – there is no intrinsic value in otm options he he he he!!!!!!!!. Of course, there is intrinsic value and time value. My point was, without time value, implied cannot be calculated?!?!?!.

I also said a constant volatility is questionable – questionable because it isn’t constant across strikes/time. Where is the confusion???? I use the Black 76 model - or is it Black-Scholes 76!!!!!!!??????

Limitations in coding?????? I’d agree 100%. I could get ‘techie’, learn C++ or even become a Microsoft MVP and where Chinos!!!!!!!!

No thanks, I’ll stick with trading, drink, drugs and prostitutes!!!!!!!!.

Are you a quant, Robert???????? I reckon you are!!!!!!!!! If I need help, I’ll give you a shout!!!!!! One should never stop learning.Thank you, once again.

Grant

Here is what I mean.....

Implying a vol -> Use inverted BS76 equation (const vol)

Pricing a option -> Use whatever model you want (with whatever vol surface you want, calculated from your implied vols above, and smoothed with whatever method)

Why use the BS76 (const vol) to imply the vol??? beacuse the market prices have the skew pricied in, hence you are implying the skew from the market prices.......
From there one can create a vol surface, smooth it and then put the vol surface in whatever model one feels most confortable with....

 

[Grant]

Robert,

Confusion abounds. Yes, vol is assumed to be constant in BS 76 (and other models). This is not my point. My point was that some quote vendors present a constant implied across all strikes - which isn't correct.

While it is an underlying assumption of the model, we know it isn't the case in practise across strikes. Hence, the skew/smirk/smile.

My implieds are derived exactly as you suggest - back out each per strike/expiry.

While the above may suggest inconsistency, as you will be aware there hasn't been any significant improvements in Black's model - at least as a starting point.

Hope that clears the air.

Grant.

 

[Robertral]

Robert,

Confusion abounds. Yes, vol is assumed to be constant in BS 76 (and other models). This is not my point. My point was that some quote vendors present a constant implied across all strikes - which isn't correct.

While it is an underlying assumption of the model, we know it isn't the case in practise across strikes. Hence, the skew/smirk/smile.

My implieds are derived exactly as you suggest - back out each per strike/expiry.

While the above may suggest inconsistency, as you will be aware there hasn't been any significant improvements in Black's model - at least as a starting point.

Hope that clears the air.

Grant.

I think one of us is off track in this......probably me reading this too quickly.......

The model I use are either a SV model or a modified BS with vol surface......but for each model I imply a vol using a const vol BS model...If I back out an implied vol using a a model that allows for skew then the IV's will be incorrect.....

Rule is: When implying a vol from the market use an inverted BS76 (const vol)....When pricing an option use a model that allows for the skew with the vol surface you generated from the implied vols (or calibrated to using a SV model or whatever model)

 

[Grant]

I think I detect a resolution. The ambiguity may arise from objectives - we need to know what the market is implying, AND a 'fair value'. From what you've said thus far, your primary concern is a consistent fair value for all strikes/expiries, hence the vol surface. SV's, etc. I think I'll leave to you (I'll probably get a headache).

For the non-mathematical (eg, myself) Goldman Sachs' Quantitative Strategies Research Notes are a model of lucidity re volatility, surfaces, etc - do a search on Google; also see Emanuel Derman (ex GS) on www.ederman.com for papers.

As a footnote, re calculation of call implied (via Black 76) I use simple iteration and compare a theoretical with the maket value, adjusting the theoretical implied until the two values converge. Similar for the puts - solve simultaneously with put-call parity. Accuracy is what you want it to be - +/- 1 point, 1/2 point; it's a trade-off with speed. It's may be crude, but effective. I'm not qualified to commment on relative efficiency or comparisons with previously mentioned methods. But it works.