Talk:Greeks (finance)/Archives/2012

Psi

I am interested in the derivative of price with respect to continuous dividend yield. I have seen on the web that this is called 'Psi', but am not sure if this is commonly accepted terminology. Can anybody confirm? —Preceding unsigned comment added by Shabbychef (talk • contribs) 18:32, 8 November 2010 (UTC)

Mamma?

Someone has written in the blurb underneath the boxed table that the table is called "The Mamma". This is clearly a joke. Not wanting to ruin the fun, but should wikipedia really contain jokes like this?194.153.106.254 (talk) 14:06, 4 October 2010 (UTC)

Comments

Anyone else agree that the definition of Vega as the "sensitivity to implied volatility" is too specific, if not inaccurate? Implied volatility by definition is an output of the pricing model. Volatility is an input, and its estimated value may be based on implied volatility from observed prices, historical price analysis, or simply the user's intuition. I've read the source from riskglossary.com, and I believe that misstated as well.

Technically you may be correct. However, in practice vega is almost always referenced in the context of implied volatility. Vega is generally used to 1) predict a portfolio's sensitivity to changes in implied volatility, and 2) attempt to explain, ex-post, the change in PnL due to movement in market vols. IMHO, it doesn't make a whole lot of sense to talk about vega in the context of estimated vol. I would leave it as is. Ronnotel 14:08, 4 January 2006 (UTC)

The definition of Vega is that it is the "derivative of V with respect to sigma" --- pure and simple. Here simgma is NOT the implied volatility (and estimated market determined quantity) but rather a prameter of the models. After Vega is defined and understood, one might well use the theoretical understanding of Vega and a market observation of the change in implied volatility to take a view about the option price, but this in not baked into the cake.

On returning to this 7.5 months later, perhaps it is better to do leave practical considerations for another time and stick to pure model definitions. I'll make the change.Ronnotel 01:22, 29 August 2006 (UTC)

Vega formula

Is the formula for Black-Scholes vega correct? At the very least it's inconsistent with the Black-Scholes page. —Preceding unsigned comment added by 217.155.45.30 (talk) 21:26, 2 April 2008 (UTC)

The formula on the Black-Scholes page doesn't incorporate dividend yield, is all. Otherwise, they are the same. Mkoistinen (talk) 10:16, 7 September 2009 (UTC)

Ordering of the Greeks

Would anyone else agree that the alphabetical ordering of the greeks is somewhat confusing? Certainly it makes the article a little unaccessible when one is immediately hit with 'Charm' - it would be much more useful to have Delta first, for example. Could it be structured as, say, first order derivatives followed by higher order derivatives? Or Common Greeks followed by Other Greeks?

This is precisely why I created the table near the top of the article organizing them into a table relating them to their base sensitivity and their 'family' and color-coding them by their order-ness (gamma, vanna, and color are all 2nd order derivatives of Delta, etc.). I hope this is helpful. Mkoistinen (talk) 10:18, 7 September 2009 (UTC)

Can the "Greeks" be empirically observed??

from actual market prices?

for example theta must be difficult to isolate?

Yet i've seen people with spreadsheets that DO determine these greeks empirically from tick prices etc? is it true?

Yes, the greeks are all very real and can be empirically observed. When an underlier changes value, the change in the option's market price changes by just about what delta would predict. However, keep in mind that market prices are stochastic - there is always some noise. Gamma, vega and even theta are also quite easy to observe as well. For instance, just an insurance policy with 11 days left is worth about 1/10 more than one with 10 days left, the value of an option *must* decrease by theta every day (all other factor's held constant). If market prices didn't move like that, there would be an opportunity for arbitrage. Ronnotel 03:43, 5 October 2006 (UTC)

Of course these observations are based on a model, e.g. the Black-Scholes model, so you wouldn't say the the greeks are "independently observable." For example, if you assume the Black-Scholes model applies (a big if, really)then all you need to know is the risk-free rate, stock price, time to expiration, strike price, and the (independent) observation of the option price; then these observations together with the model imply the volatility, vega, theta, gamma, etc. So it's hard to say that you are really observing all "the greeks." Smallbones 12:13, 5 October 2006 (UTC)

I wouldn't necessarily say that the Black-Scholes model is the most accurate, but certainly it is possible to measure and predict option behavior and pricing using models (tree-based, Stochastic volatility models seem to work best IMHO). I observe and rely on these behaviors every day. There really is no question about whether the greeks are real or not. Ronnotel 12:36, 5 October 2006 (UTC)

Comment on vega gamma

I reverted a comment on vega gamma that seems to imply a disconnect with text book definitions. However, I think commenter is refering to vega, which is described above as the first derivative. Ronnotel 21:21, 1 December 2006 (UTC)

So what Kasper is anyways?

dunno - never heard of it. By all means if something seems incorrect or poorly explained, feel free to take corrective action. Perhaps it should be removed until it can be substantiated? As long revisions are explained, no one will get too fussed. Be Bold! Ronnotel 20:56, 6 February 2007 (UTC)

Etymology of vega

Can anyone find a reference for the etymology or origin of the term "vega" as applied in finance? I have heard it said that "it's not a Greek letter but it sounds like one" and that it is a humorous reference to the Chevrolet Vega, but have no references for these, and they could be conjecture. Nbarth 22:58, 9 June 2007 (UTC)

I believe it is very simply a greek-letter sounding name that begins with "V", since it is measuring the sensitivity to Volatility. Just like Theta is for Time and Rho is for Risk-free Rate. The relationship to the Chevy car is, I am sure, coincidental. There are many other things labeled with "Vega" such as the star. Mkoistinen (talk) 17:01, 1 April 2009 (UTC)

Well, since the story was recently added on April 1, and for some reason removed, that would support Mkoistinen's view. This has always been the standard joke on the subject and it follows a certain colorfulness in finance terminology. BTW, Mk's additions on April 1 were obviously not April Fool's Day jokes, but he should get himself a User page to avoid the redlink. 80.65.84.49 (talk) 11:25, 3 April 2009 (UTC)

Beta?

Should beta be mentioned here? It's a greek letter in finance maths...

Interesting point, however the flavor of this article definitely indicates it is targeted to those measurements of risk specific to derivatives. I would say definitely not, however we might consider changing the article's name to 'Measures of derivative risk', or similar. Ronnotel 11:26, 26 July 2007 (UTC)

I put both alpha and beta under "See also." I don't think it really should go beyond that in this article, as Ronnotel says. In fact, if others want to remove this I wouldn't mind, but it would seem to fit here the best. Smallbones 13:15, 26 July 2007 (UTC)

What Is This??

It would be really great if someone could write a short blurb explaining what the "Greeks" are. I've done a bit of finance but this article is written at a pretty high level. I'd appreciate a version or at least supplementary text that isn't so math-based. Alpha and Beta are pretty key concepts to investing and a simpler explanation shouldn't be too hard for someone who understands this. —Preceding unsigned comment added by A3camero (talk • contribs) 03:25, 12 April 2008 (UTC)

I'm giving it a try. Also, I've moved the expressions over to the right in little "sidebars" to improve the readability of each blurb. Mkoistinen (talk) 18:19, 1 April 2009 (UTC)

Epsilon?

In the bank where I work epsilon is the dividend risk on (equity) derivatives, but I am not sure if it is a generally accepted term. Anybody else know if this is a general term, and if so should it be added? —Preceding unsigned comment added by 193.108.78.10 (talk) 15:41, 12 August 2008 (UTC)

Higher-order derivatives

I just noticed that in the higher-order derivatives section a number of risk measures refer to concepts in quantum physics. While I can understand the meaning (for example) of Delta decay from the mathematical representaion - d2v/dsdt - I'm very curious how is it correlated with "charm". I bet it would make a useful addition to the article as well. —Preceding unsigned comment added by 192.147.58.6 (talk) 16:41, 26 August 2008 (UTC)

I do not believe that Charm (finance) has any relation to Charm (physics) except that, in both cases a label was required to represent the underlying concept. It wouldn't surprise me, though, if some people label the even higher-order derivatives with other quark-like names such as Beauty (Bottom) and Truth (Top) or Strange, but I haven't come across them yet. Mkoistinen (talk) 12:45, 2 April 2009 (UTC)

Description of changes made on 1-April-2009

In the previous version of this page, the section heading "Higher-order and Cross-derivatives" doesn't really work for these reasons: 1. Gamma is a higher-order sensitivity, but was listed above and not in this section; 2. There wasn't really any distinction between "higher-order derivatives" and "cross derivatives"

I've also added some more description of why the Greeks are important and linked their use to the concept of portfolio management via delta- and gamma-hedging. This should help the reader understand why these Greeks exist and why others may not.

Added a table to illustrate the relationship between each Greek to both the primary BSM model (Price, Time, Volatility and Rate of risk-free investment) and to (Value, Delta, Gamma and Vega). Although this is a bit strange to organise Greeks partly by the Greeks themselves, I believe it is a useful way to relate the Greeks.

Finally, I've re-written some of the descriptions of the Greeks themselves to be more uniform. More work must be done here. Mkoistinen (talk) 17:14, 1 April 2009 (UTC)

Please note that there are now a lot of links to these greeks

I have made a number of links throughout Wikipedia into this page such that they link to in-page anchors on each greek's name. For example, Delta (finance) redirects to this page at the Delta subheading. The reason this is being done is to allow a graceful shift to the use of independent pages for each greek, if needed in the future. For this reason, please do not rename any of the greek's named headers without fixing all these links. Mkoistinen (talk) 12:06, 5 April 2009 (UTC)

Only properly cited greek names, please

Following Gxti's decision to simply delete some of the uncited greeks (which incidentally wiped out a lot of my own work fixing up and properly incorporating those greeks, even though I didn't add them), I have now gone in and added at least one citation to nearly all of them, no matter how common they are. Can we adopt a policy now of only adding greeks that have a properly cited reference?

There were a few bogus entries in there, apologies if I threw out some legitimate ones as well. As mentioned they were uncited and relatively obscure. -- gxti (talk) 21:15, 25 May 2009 (UTC)

ADD synonyms, not replace the existing!

Also, can we not make arbitrary decisions to replace the names of greeks (i.e., 'Ultima') with the name *you* prefer/like/use (I.e., 'Froota'). If you have a synonym for an existing greek, please ADD it to the existing named greek description as is the case for many of these. Mkoistinen (talk) 10:19, 7 September 2009 (UTC)

Ultima definition

Ultima's definition was wrong. Either you state its D^3V/DSigma^3 and D^3V/DSpotDSigma^2. But was corrected thanks —Preceding unsigned comment added by 87.97.86.91 (talk) 10:10, 19 July 2009 (UTC)

Strike

Does there exist a Greek for change in price due to change in strike? Although strike is fixed in a vanilla option. Angry bee (talk) 19:05, 8 December 2009 (UTC)

Yes, dual delta, dual gamma. See discussion below and edits on main page. It's also not hard to confirm differentiating by hand. —Preceding unsigned comment added by 99.255.90.205 (talk) 17:12, 30 January 2010 (UTC)

Dual delta and dual gamma appear in the formula table, but only the definition of dual delta is briefly mentioned under "Delta" and the definition of dual gamma is not explained. These should be added as a bullet point under "First order Greeks".

Is the delta example correct?

I'm just trying to teach myself about Delta from the page. I'm just a developer with rusty maths, so I may be barking up the wrong tree, but, regarding the example:

"For example, if an American call option on XYZ has a delta of 0.25, it will gain or lose value just like 25% of 100 shares or 25 shares of XYZ as the price changes for small price movements."

If I've understood (a big if) then isn't the last comma-separated statement true of 100 options, rather than a single option as implied by the "an ... option" in the pre-comma section? Shouldn't it read:

"For example, if an American call option on XYZ has a delta of 0.25, then 100 such options will gain or lose value just like 25% of 100 shares (i.e. 25 shares) of XYZ as the price changes for small price movements."

(The wording still seems clumsy, but my query is whether the "25 shares" equivalence is true of a single or 100 options....)

Cheers, Tony —Preceding unsigned comment added by 199.43.19.222 (talk) 04:40, 21 June 2010 (UTC)

sensitivity of delta to strike

In order to correct some pricing model inaccuracies in the far OTM and ITM strikes, I've developed a quick n' dirty B/S-based formula for the sensitivity of call delta to strike, or ddC/dSdK. It turns out to be similar to the B/S formula for gamma, except replacing S with (-K). I'd like to verify that I've cranked my derivatives correctly. Has anyone ever seen a derivation of ddC/dSdK? If I can find a reference, I'd like to add this formula to the page. Ronnotel (talk) 16:56, 3 December 2010 (UTC)

Formulas on right side

From my point of view the formulas for the Greeks should be alligned left. Now they seem to be hiddn there, or at least unusual to read as mathematican... --2.200.171.6 (talk) 11:55, 28 January 2011 (UTC)

Formula complexity

The section discussing the put <-> call delta calculation seems unnecessarily verbose and complex.

If the value of delta for an option is known, one can compute the value of the option of the same strike price, underlying and maturity but opposite right by subtracting 1 from the known value. For example, if the delta of a call is 0.42 then one can compute the delta of the corresponding put at the same strike price by 0.42 − 1 = −0.58. While in deriving delta of a call from put will not follow this approach eg – delta of a put is −0.58 and if we follow the same approach then delta of a call with same strike should be −1.58. so delta should be = opposite sign ( abs(delta) − 1).

Why not just say that:

${\bar {\delta }}=\delta -{\frac {\delta }{|\delta |}}$

Where $\delta$ is the put or call delta for an option, and ${\bar {\delta }}$ is delta for an option of the opposite side (but with the same strike price, underlying and maturity).

eg.

$\delta (C)=0.42\Longleftrightarrow \delta (P)=-0.58$ —Preceding unsigned comment added by 124.148.176.11 (talk) 12:11, 15 February 2011 (UTC)

Black-Scholes Section

Hello, I believe there is a mistake on this page. The section titled "Black-Scholes" the value and Greek formulas are actually those for the Black model, which is slightly different. Does anyone agree? If so can a more seasoned Wikipedea update this please? —Preceding unsigned comment added by 83.217.118.146 (talk) 18:06, 13 May 2011 (UTC)

Vega ν section

Never states the time scale of the volatility measure. I believe it is the annualized volatility as stated here: http://www.deltaneutraltrading.com/vegabasics.html

According to Volatility (finance)

this measure is scale-dependent, so it seems that it would matter to specify the time period. --Pomoo (talk) 22:16, 1 July 2011 (UTC)

Delta as proxy for probability of expiring in the money

To the anonymous user who felt that it was OK to simply delete a section. Rather than delete this section, why not simply add some referenced, supporting material to justify NOT using Delta as a proxy for probability of expiring in the money? I have added references to materials that support this already, and I don't think it is appropriate for anyone to remove material because you think it's "bullshit". Mkoistinen (talk) 15:20, 7 January 2010 (UTC)

I just added material to elaborate on and somewhat undercut the idea that delta = P(ITM). Without doing the derivation, here is an intuitive way to think about it: Consider that a vanilla call can be decomposed into a portfolio of two binary options: long a stock or nothing option, short a digital option for the amount of the strike. This is what the B-S call formula happens to look like: S * delta - K * dual delta. K times P(ITM) is exactly what the digital option is worth. While this does not constitute a proof ("proof by coincidence"!), it does happen to coincide with the mathematical facts. For the sake of giving an actual citation, here is one: https://cboe.com/Institutional/pdf/ListedBinaryOptions.pdf this is a research note for product development on the CBOE, for digital options (written by Lehman Brothers (rip) quants). The last line on page 5 is the statement that Dual Delta = P(ITM) = value of digital option on $1. The continuing discussion on page 6 also states that Delta <> P(ITM).

Finally, to convince oneself that the ATM does not necessarily (or even typically) equal .5, calculate delta for an ATM option one year out, on an underlying of $1,000, with a volatility of .2. At this price level and volatility, the asymptote at zero does not come into play in any noticable way. Yet the delta of the option well approach and exceed .60 as you increase the interest rate (or decrease the yield if there was one), and, more importantly, raise the volatility or add time. The higher-than-fifty delta is mainly a result of the lognormal distribution, not the stop-out at zero.

Final finally, here is a citation (google books internal) to the statement that Dual Delta is d(c)/d(k). http://books.google.com/books?id=2sGwSAfA8eAC&pg=PA124&lpg=PA124&dq=%22derivative+with+respect+to+strike%22&source=bl&ots=Ir-ccuVuAX&sig=AFDgYzYcCUvqohT0WzkFxVzRpFI&hl=en&ei=ERJiS8TrOY3O8QbS5YWmAg&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBAQ6AEwAQ#v=onepage&q=%22derivative%20with%20respect%20to%20strike%22&f=false

I haven't included either of the citations given here in the page, b/c they both seem somewhat ephemeral.

I am skeptical of the claim made in the article that Dual Delta = P(ITM)? Note that the formula is given for Dual Delta in the section below; the formulas given for the put and the call do not sum to 1 after taking absolute values. For a call and put with identical input parameters, shouldn't it be the case that P(Call_ITM) + P(Put_ITM) = 1? Can someone please clarify this seeming discrepancy and provide some supporting documentation? — Preceding unsigned comment added by 173.20.242.205 (talk) 05:32, 28 July 2012 (UTC)

PS I'm pretty sure Dual Gamma needs a minus sign, but I'm not going to put it b/c I'm so rusty on doing even simple math. —Preceding unsigned comment added by 192.234.99.1 (talk) 15:55, 29 January 2010 (UTC)

"Vega is the most substantial greek for options and futures."

I don't know what makes a greek sensitivity "substantial". But whatever it might be--it does not apply to futures. —Preceding unsigned comment added by 192.234.99.1 (talk) 16:21, 29 January 2010 (UTC)

Charm's formula?

I'm using the formula presented here for Charm at the bottom of the page in an application. I notice that my results are opposite what they should be meaning I get what I expect when I multiply the result by -1. I further notice that the formula for Theta -- which works well for me -- has, in its third term, +q for calls and -q for puts. I wonder if the formulas for Charm should have the same, +q for calls (rather than -q) and -q for puts (rather than +q) in its first term? Can someone double check (I'm afraid I don't have any reference materials that would show this myself). Mkoistinen (talk) 10:05, 7 September 2009 (UTC)

FORMULA FOR CHARM seems to be INCORRECT — Preceding unsigned comment added by 158.180.128.10 (talk) 11:12, 12 November 2012 (UTC)

Yes, I concur. My derivation (backed up by Wolfram Alpha) comes out very different. I haven't been able to find any published sources for this, however, so I'm reluctant to swap in my version. Users beware. Ronnotel (talk) 20:04, 7 December 2012 (UTC)