Talk:Greeks (finance)

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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)

[edit] 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)

[edit] 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)