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22 votes
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Gamma Pnl vs Vega Pnl

For an option with price $C$, the P$\&$L, with respect to changes of the underlying asset price $S$ and volatility $\sigma$, is given by \begin{align*} P\&L = \delta \Delta S + \frac{1}{2}\...
Gordon's user avatar
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20 votes
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American Options relation between greeks

No, you should not expect such a relationship to hold in general. The reason is that American options have an "exercise barrier" which European options don't, and this results in different prices and ...
Chris Taylor's user avatar
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17 votes
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Barrier option (autocallable) Vega profile

You have a multidimensional problem - there isn't an answer of "this is what the greeks look like" for all cases, because it depends on the various levels of the different parameters. For example, if ...
will's user avatar
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12 votes
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Link between Vega and Gamma

Under the Black-Scholes model, \begin{align*} Gamma &= \frac{N'(d_1)}{S \sigma \sqrt{T-t}}\\ Vega &= SN'(d_1) \sqrt{T-t}. \end{align*} Then, it is easy to see that \begin{align*} Vega = S^2 \...
Gordon's user avatar
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9 votes
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Mathematical underpinnings of the square root of time rule

For any process with independent increments, by the very fact of statistical independence the variance of $x_{t3}-x_{t1}$ is going to be the sum of the variances of $x_{t2}-x_{t1}$ and $x_{t3}-x_{t2}$ ...
Alex C's user avatar
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9 votes

Expectation of Gamma times S$^2$ in Black-Scholes model

The conjecture is true when the interest rate is zero. Note that, from this question, under the Black-Scholes model, \begin{align*} \Gamma(t,S_t) &= \frac{N'(d_1(t))}{S_t \sigma \sqrt{T-t}}\\ ...
Gordon's user avatar
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8 votes
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Vol, Gamma, Vega -- essentially all the same?

They are not the same, but they are related. Gamma is sensitivity to realized volatility. Vega is sensitivity to implied volatility. Vanilla options are always long gamma and long vega, so they are &...
Chris Taylor's user avatar
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6 votes

Gamma Pnl vs Vega Pnl

Not sure this is a valid question! Gamma p/l is by definition the p/l due to realized volatility being different from implied. Vega p/l is by definition the p/l due to moves in implied volatility. ...
dm63's user avatar
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5 votes
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Question about the vega of a stock

Vega is the partial derivative of the option price (as a function of parameters -- current stock price $S_t$, strike price $K$, implied volatility $\sigma$, etc.) with respect to $\sigma$ -- holding ...
RRL's user avatar
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5 votes
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Long/Short Vega and Option Positions

The risk exposures/sensitivities of long and short positions always have different signs. This has to hold since derivatives are zero sum games. Vega is always positive for a long position in a ...
LocalVolatility's user avatar
5 votes

how to calculate vega in stochastic vol?

This is an interesting question. Peter A is correct that SV is typically combined with LV these days to get the so called SLV (stochastic local vol model). There is no obvious definition for Greeks ...
AKdemy's user avatar
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5 votes
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How do we hedge option vega practically?

If you are a market maker, your primary Vega hedge is to sell Vega to other clients. You do this by being the best offered side price in the market, so you will attract the next piece of business. ...
dm63's user avatar
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4 votes
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Volatility products and constant vega

Here is a document that will answer some of your concerns. There are many other good reads out there but this one is a nice one to get started with. In case the link is broken at the time one reads ...
Quantuple's user avatar
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4 votes
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Vega and Gamma signs

Usually vega and gamma go in the same direction, but you can have opposite exposure in a calendar spread. For an ATM option, vega decreases closer to maturity while gamma increases. If you implement ...
fni's user avatar
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4 votes

Is Complete Vega Elimination Possible?

Well , complete elimination of even Delta is not possible, forget about Vega. When I say this , I'm talking about the trouble you'd face if you keep dynamically hedging your position from time to time....
HyperVol's user avatar
  • 308
4 votes

Is Complete Vega Elimination Possible?

Constant Vega Requires Options Weighted Inversely Proportional to the Square of the Strike. E.g. if you have the following portfolio of options: \begin{equation} \int_{S_i(t)}^{\infty}\frac{2\Big(1-\...
phdstudent's user avatar
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4 votes

Long/Short Vega and Option Positions

No, you are incorrect. A deep in the money option is long vega. It's not just about the probability of being in the money, it's about how far in the money it is. Your reasoning is correct if we ...
dm63's user avatar
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4 votes
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Why do we need to calibrate vega?

It seems like he is assuming that the shorter term volatilities change more than the longer term ones and the relatively sensitivity is proportional to $1 / \sqrt{T}$. Thus, this hedge is not against ...
LocalVolatility's user avatar
4 votes

Why do traders think about options in terms of volatility?

Volatility is in effect what you are trading in options and the one unknown quantity in options valuation. The other inputs in option valuation: (1) Spot Price: observed in the markets, (2) Strike: ...
AlRacoon's user avatar
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4 votes

Vega in the Heston model

Zhu makes sense to me. The vega cash in Black-Scholes corresponds to a shift of the vol surface by 1%. If you bump only $v_0$ in Heston, you bump only the short maturities, and if your structure is ...
jherek's user avatar
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4 votes
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Calculating vega in Heston?

Let $V$ denote the variance and $v$ the volatility, i.e. $V=v^2$. The natural argument for the option price under a stochastic volatility model is typically the variance, i.e. $C_\text{SV}=C_\text{SV}(...
Kevin's user avatar
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4 votes
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Relationship between VIX and Vega

Vega is the option's price sensitivity to the volatility (i.e. IV). In the graph below, vega is shown to be a strictly positive function in volatility, which means that at any point in the graph (i.e. ...
Jan Stuller's user avatar
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4 votes

Relationship between VIX and Vega

VIX almost always only spikes when SPX goes down as @Jan Stuller also mentions in a comment. Insofar the question is a bit counterfactual. I frequently use twin axis in the charts that follow. The ...
AKdemy's user avatar
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3 votes
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European option Vega with respect to expiry and implied volatility

To keep notations uncluttered, consider that $r=q=0$ in what follows, while focusing on the particular case of an ATM option i.e. $K=S$ (otherwise use the same reasoning with $K=F(0,T)=Se^{(r-q)T}$ i....
Quantuple's user avatar
  • 14.6k
3 votes

Is Complete Vega Elimination Possible?

In general only non-linear instruments, like options, posses vega. Vega is always positive, no matter the directional component. So when you are long either a call or a put option you are long vega ...
vonjd's user avatar
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3 votes

Simulation of the Vega in Heston model (for Asian Option)

Chan, Jiun Hong and Joshi, Mark S. and Zhu, Dan, First and Second Order Greeks in the Heston Model (December 26, 2010). Available at SSRN: https://ssrn.com/abstract=1718102 or http://dx.doi.org/10....
Mark Joshi's user avatar
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3 votes

American Options relation between greeks

One way to think of American-exercise options is to break their value $V_A$ down into a value due to the european exercise, $V_E$, and a "premium" due to the possibility of early exercise, $V_P$ $$ ...
Brian B's user avatar
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3 votes
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Calculating Implied ATM Volatility with Vega

Assuming you mean inverting the Black Scholes Vega, it does seem possible: Take the Vega formula: $V = S \sqrt{\tau} n{\left (d_{1} \right)}= S \sqrt{\tau} \frac{1}{\sqrt{2 \pi}}e^{-0.5 d_1^2}$ ...
Magic is in the chain's user avatar

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