Implied volatility and Moneyness

[grantx]

Gentlemen,

I'm having difficulty with this. Maybe some kind soul will take pity.

Assume a 5000 strike is 250 points itm and trading at 20% iv.

A month later the 5000 strike is 100 points otm but iv is still 20%.

If I'm recording the iv on a daily basis for this particular strike, a chart would display a flat line, ie 20% only over the relevant time period. But the underlying has shifted.

Therefore, comparatively, we are looking at two different options (aren't we?) - 250 points itm, 100 points otm.

How can the shift in the underlying be reflected via an adjustment to the iv figure? I was thinking along the lines of perhaps incorporating the degree of moneyness but unsure as to the correct method.

This would also help in historical comparisons as to whether an option is cheap or expensive without referring to every underlying level and the degree of itm/otm.

Grant.

 

[NotQuiteRandom]

Hi,

Every time you record an implied vol, also record the delta of the option for which it is the vol. That way you have a ready point of reference which factors in the strike and expiry time in the way that matters (monyness).

In your database you should juxtapose the two. When plotting a vol surface you should use vol on the y axis, delta on the x and time on the z. Strike is not so relevant as it is the delta we are interested in really. In the OTC fx markets all fx options are quoted in terms of delta rather than strike for this reason.

NQR

 

[Profitaker]

How can the shift in the underlying be reflected via an adjustment to the iv figure?

Given that the implied vol is observed in the market place, why would you want to adjust it because the underlying has moved ?

Not sure what you’re trying to plot, and why ?

Every time you record an implied vol, also record the delta of the option for which it is the vol. That way you have a ready point of reference which factors in the strike and expiry time in the way that matters (monyness).

You would, but a change in IV would then give the illusion of a change in moneyness when perhaps none actually happened. For example, if an OTM option saw it’s IV spike (for whatever reason) the delta would move towards 1.0, indicating a change in moneyness when none actually occurred.

Again, I’m not exactly sure what Grant is trying to plot.

 

[NotQuiteRandom]

Quote:
Originally Posted by grantx View Post

How can the shift in the underlying be reflected via an adjustment to the iv figure?
Given that the implied vol is observed in the market place, why would you want to adjust it because the underlying has moved ?

Not sure what you’re trying to plot, and why ?

Quote:
Originally Posted by NotQuiteRandom View Post

Every time you record an implied vol, also record the delta of the option for which it is the vol. That way you have a ready point of reference which factors in the strike and expiry time in the way that matters (monyness).

You would, but a change in IV would then give the illusion of a change in moneyness when perhaps none actually happened. For example, if an OTM option saw it’s IV spike (for whatever reason) the delta would move towards 1.0, indicating a change in moneyness when none actually occurred.

Again, I’m not exactly sure what Grant is trying to plot.


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Profitaker, you are right that "if an OTM option saw it’s IV spike (for whatever reason) the delta would..." increase. This however reflects a change in the market's expectation of the volatility at that strike / tenor. This perceived change in probability is reflected in the change in delta as a consequence of the vol spike. In turn, this relates to the degree of moneyness.

Think of it like this, the (spot) market need not move for an effective change in moneyness where we qualify moneyness in terms of the probability of the market reaching a certain point. For example: take an option on EUR/USD which is 50 points OTM with an IV of 6% and a delta of 20. If the IV spiked up to 11% and the delta therefore moved up to, say, 36 we are no longer looking at the same option despite a static spot price. The probability (albeit only the market's perception of it) has changed.

Moneyness is only relevant as it relates to probability which, in this instance, is quantified in terms of implied vol rather than absolute number of points from ATM.

Grant, when plotting a surface at time 1 (t1), t2, -> tn, record the deltas and the implied vols, then you will have a stable point of reference to compare through time. A 25 delta call is always comparable to a 25 delta call, regardless of strike, where spot is trading or time.

NQR

 

[Profitaker]

Think of it like this, the (spot) market need not move for an effective change in moneyness where we qualify moneyness in terms of the probability of the market reaching a certain point.

Sure, but I'm not entirely convinced that Grant wanted to plot moneyness as a probability.

Grant ?

 

[grantx]

NQR,

Thank you for the solution.

PT,

“why would you want to adjust it (iv)”. I think the difficulty was due to the ambiguity of a half-baked and badly expressed thought – I was looking for a solution to an ill-stated problem. So you’re correct; changing the iv isn’t appropriate, but changing the frame of reference from strike to delta is, as per NQR.

My problem was an inability to reconcile what I perceived to be shortcomings in comparative iv’s for the same strike(s) – same iv’s but over time, varying degrees of moneyness.

The reference to flat line on a chart was for illustration, not intent, ie iv flat, but underlying dynamic. I’m not trying to plot anything (however, NQR’s suggestion is something I should consider).

Perhaps the question could be re-stated as, What price moneyness? I can see if iv for the 5000 strike is more expensive or cheaper than previous in iv terms, but is the cost of 25% iv, 100 points itm more or less than 25% iv, 100 points otm?

Moneyness-delta-probability – in this context I think any distinction is academic.

I will return to this tomorrow when I have more time.

Until then, thank you gentlemen.

Grant.

 

[grantx]

The next problem is recording the data consistently.

Attached is a sample Excel file. From column C, I need to retrieve the iv corresponding to the delta in column E. Index, Match, VLOOKUP functions don't seem to work. Any ideas?

To overcome the problem of matching precise figures(column E) with imprecise figures (column B), ie 0.89 delta in column E will not match 0.89 in column B because the latter may actually be 0.8764 but rounded, the figures in columns B will be of the format =Left(delta,4). So =Left(0.8764,4) = 0.87). Hopefully, this will work.

Thank you.

Grant.

Thank you.

Grant.

 

[swandro]

Hi Grant

Here is a solution. You CAN use VLOOKUP, but there are a couple of things you need to do to make it work. The reason it is not working is that the number in column B is not actually a number - I think it is stored as text. So if you compare it to a table of numbers, it does not match. This can be fixed by using VALUE (B3), for example, in the VLOOKUP function. This will treat the contents of B3 as a valid number.

Secondly, I would recommend that you create a copy of columns E and F so that you can specify the values in E with 2 decimal places. This means that with VLOOKUP you can force it to look for an exact match. It is capable of returning the nearest value, but to do that I think the values have to be in ascending order, and you have them in descending order.

So, in H3, type the formula: ROUND(E3,2) and copy down. This will enter the E values into column H with exactly 2 dps. In I3, copy whatever values you need.

Then, in another cell: VLOOKUP(VALUE(B3),H3:I99(i.e. the exact range you are working with),2,FALSE).

The FALSE will make it return an exact match.

Hope this helps

Rob

 

[A Dashing Blade]

. . . The reason it is not working is that the number in column B is not actually a number - I think it is stored as text. . . .

Yup.

eg, type this into cell H3 . . . =VLOOKUP(ROUND(E3,2),$B$3:$C$26,2,FALSE)

edit the cell, highlite the $B$3:$C$26 bit and hit F9 . . . you should see this the formula turn into this . . .
=VLOOKUP(E3),{"0.89",0.17701762706188;"0.85",0.173442641395381;"0.82",0.186694268656122;"0.75",0.196593564803331;"0.76",0.179245858523216;"0.70",0.189145856011291;"0.69",0.173065679854228;"0.63",0.173013066778798;"0.60",0.167208644563233;"0.55",0.168629820560902;"0.50",0.162523384137264;"0.44",0.168396830920471;"0.40",0.159927925097956;"0.35",0.160126818299376;"0.29",0.16188433826103;"0.25",0.155827193027214;"0.21",0.163922432783392;"0.17",0.15998574899584;"0.14",0.154000360543472;"0",0;"0.09",0.163721432345595;"0",0;"0.05",0.157332008562023;"0",0},2,FALSE)

ie the F9 key stroke has evaluated the highlited formula input.

See the quote marks all over the place? That's excel's way of saying text.

You can use the VALUE() function to turn text into numbers and, as swandro suggests, the ROUND() function to convert to 2dp's. Doing it in one hit would obviously be something like =ROUND(VALUE(A1),2)

 

[grantx]

Rob,

Thank you for the solution. It certainly works but I wanted to avoid more duplication, ie copying columns E and F.
I don’t know why Column B should be text – it is the result of formulae.

Keeping with the original format, but as per your suggestion, I rounded to 2 (=round(X,2)) the formulae for delta; thus, delta in column B to 2 decimal places.

However, I also got the ‘#N/A’, which needed to be eliminated; and if there is no iv, then the cell should also be blank.

This is the result (column F):

=IF(ISNUMBER(VLOOKUP(E3,$B$3:$C$26,2,FALSE)),VLOOKUP(E3,$B$3:$C$26,2,FALSE),"")

Please refer to y.xls.

Note I have change the format of delta to my preference. Also, the deltas are the result of copy, paste, value from the formulae as per the original. Strange.

Thank you, once again.

DB,

Is this safe? I’ll give it a go and see.

Grant.

 

[grantx]

Gentlemen,

Continuing from above, I wonder if someone can solve the latest proble?

Please refer to the attached x.xls.

The values in column K are from C-D. However, despite identical formulae and formats, nothing appears in column N for columns G-H.

Any suggestions?

Grant.

 

[swandro]

Sure. The ISERROR condition is proving to be true. Reason? The values in column G are not being treated as valid text values. For example, if you just type .84 in cell G4, you will get a value in N19. So just retype the values in column G and you are back in business.

 

[grantx]

Swandro,

Thank you for your suggestion.

The problem is, the appearance of the figures in column G is random, ie contingent on a delta trading – no trade, no delta.

Further, though not shown on x.xls, theoretically there are almost 100 values - .99 - .01; multiplied by four expiry months = c 400; multiplied by two (calls and puts) = a randomly fluctuating figure of between 0 and 800.
possible values.

Re-typing these would be too much, I feel.

Despite the columns being identical in being identical in format, I decided to look outside the immediate tables. And there it was: deltas for the calls included =round(x,2), but absent for the puts. Now rectified, all’s well.

I feel bad about asking the question, you take the trouble to reply, and I find an alternative solution. Sorry about that. But it is appreciated.

Grant.