Implied volatility calculator

Hello,

Does anyone have the formula for calculating IV on US options?

I'm looking for calculating the IV on all my options in my database for educational purposes.. any idea?

FP,

There isn't a formula - you have to use iteration.

Grant.

Fp,

You can you use a variety of models for this!.
E.g Black and Scholes and CRR.
Each model will generate different numbers. Thus use with caution.

AJJ

AJJ,

Regardless of the the model used, you will still have to back out via iteration, eg guess-work or Newton-Raphson (efficient guess-work).

Grant.

Determining the IV per strike

Grantx,

What do you mean with back out via iteration?
Indeed regardless of the model used, you must do efficient guess work.

What I meant was:
In order to accurately ‘determine” the IV for one strike you must determine the IV for the whole expiration. If you do not do this the IV outcome will most likely contain a lot of misleading information.
The way I would follow for calculating / determining the IV per strike is as follows:

Steps:
1. chose option model
2. Calculate Future price of underlying (use expiration date) in order to find the ATM strike
3. value ATM straddle of that strike at market prices for respective expiration
4. “Determine” volatility of that strike
5. Determine yourself a logical skew line (this is very important because establishing the IV for one strike is mostly less accurate then establishing it for 5strikes).
6. Use that skew line to determine your theoretical prices for all strikes in respective expiration.
7. Check the difference per strike between theoretical and market prices.
8. If your prices in comparison to the market coincide “reasonably” (use logic here) than you have a better understanding of the whole expiration and thus the volatilities per strike.

Hopefully this helps.

AJJ,

The procedure you suggest seems to be the standard re surfaces.

The method I've used is to determine iv from the last trade prices, extrapolate from these and fill the gaps. Possibly lacks the precision and cohesion of your model but mapping surfaces is beyond my capabilities.

Good Trading,

Grant.

Online risk manager.

Grantx,

Thanks for your reply.

I am curious to here how you would determine the IV.

Meanwhile I would like to mention that I have build on online option calculator.
The calculator is free and open to anyone who knows how the greeks work.
On this site you can enter entire strategies (included stock positions) and concrete dividends.

I have built the site with two friends in the evening hours (ex market makers). We just went online but still have some small bugs to fix.

please let me know what your think of the site. (straddleplanner.com)

AJJ

Alex,

My interest is/was index options, specifically DAX. I was building a daily history of iv's for all options traded every day. When I had a sufficient sample (1-2 years?)this would form the basis for research into volatility plays.

All the inputs were known - underlying, strikes, rate, days to expiry - so it was simply a case of solving the iv's via the Black '76 model with a Newton-Raphson calculation for the iv. I would also record delta, theta, vega and gamma. This was done via Excel, dde's and VBA.

It was suggested that recording data against delta, rather than strike may also prove useful. The reason being recording the iv against strikes omits certain information, ie the degree of "moneyness". Again, I don't have a sufficient sample to extrapolate.

I've looked into mapping surfaces but decided the it was beyond my maths level.

Access is denied to your site.

Grant.

Math levels

Grantx,

Thanks for the documentation.

By the looks of your study it seems to me that your math skill are way higher than mine.
The way you determine the IV, is based on the past.

Maybe article of Gemmill could be of interest for you.
Gemmill G.”Did option traders anticipate the Crash? Evidence from volatility smiles in the U.K. with U.S. comparisons”.The Journal of Futures Markets. Hoboken. Dec 1996. vol 19. iss. 8. blz 881.

What went wrong with entering the straddleplanner.?

Regards,
AJJ

Alex,

"your math skill are way higher than mine" Can I have a job as an MM?

My approach to iv's is based on Last Trade (of the current day), and strictly speaking is the past. However, I think to use traded prices reveals what people are currently willing to sell/buy rather than what the mm’s are bidding/offering, which may be different. And of course, once you have the Last Trade iv and the underlying changes, you know what the theoretical value should be when there are no further trades in that particular option.

The reason I don’t use current market quotes to determine iv’s (at least for DAX options) is the irregularity of updating quotes, especially relatively deep itm. Some may be days old and while it shouldn’t be difficult to detect this by referring to time/date, it ads a further layer of complexity to a somewhat already large pricing and analysis model.

I've read plenty of papers re the predictive powers of iv's and they all conclude it's basically zero. However, I will look up Gemmill's work.

I’ll try again with straddleplanner.

Grant.

Gemmill and Implied volatility

Grant,

I've read plenty......basically zero.
Gemmill will not change this view, so don't bother to read it.

From a market maker point of view I would say that the best information is received from comparing IV over multiple strikes and expirations. All strikes are priced in relation to the next strike.
Deep in the money strikes are indeed difficult to track as trading activity in those strikes is low and more important the premium in those strikes is to low to work with.
Therefor in my opinion the most and best information lies in the atm strikes which are trade most heavily.

With regard to the straddleplanner option manager: you need to load the adobe flasplayer to continue and before you click on try it out.. first click on the bottom of same page on I agree (a legal thing).
What kind of position manager do you use now?

Regards,

Alexander

Alex,

Attached is an example of my IV calculator.

This is from close of business 10 Aug 07. Cash was down 262 points over two days, thus high put (last trade) iv's.
Blank cells equals no trades.You'll need to scroll down to all data.

Grant.

Grantx,

Your sheet is not quit clear to me. Therefor I have some questions.

If I look at the 7400 strike, I see lower vols in the calls than in the puts. This sounds like a arbitrage opportunity.
What was the index price when you took this snapshot?
Also in the 7050 strike I see some irragularity in IV for sep.

Regards,

Alexander

Alex,

This isn't a "snapshot". As I've explained, the iv's are derived from Last Trade. The arbitarge opportunities don't exist - as the market was down over 250 points over two days, puts will have a high iv and will trade more than the calls (usually). Any business done in the calls was probably earlier in the day. Indeed, there could 8 hours difference between a call trading and its equivalent put.

I'll e-mail the original input sheets.

Grant.