Questions tagged [vega]
The vega tag has no usage guidance.
101
questions
20
votes
2
answers
31k
views
Gamma Pnl vs Vega Pnl
Why does Gamma Pnl have exposure to realised volatility, but Vega Pnl only has exposure to implied volatility? I am confused as to why gamma pnl is affected (more) by IV and why vega pnl isnt affected ...
- 2,562
14
votes
2
answers
17k
views
Link between Vega and Gamma
"The vega is the integral of the gamma profits ( ie expected gamma rebalancing P/L) over the duration of the option at one volatility minus the same integral at a different volatility......
- 2,562
10
votes
2
answers
2k
views
Expectation of Gamma times S$^2$ in Black-Scholes model
Can somebody prove that:
$$E[S_t^2 \times \Gamma(t,S_t)] = S_0^2 \times \Gamma(0,S_0)$$
where $S_t$ follows a lognormal process as in the Black-Scholes model, and Gamma is the second derivative $\...
- 101
8
votes
2
answers
9k
views
American Options relation between greeks
Considering an American option in a Black-Scholes model, is there a relation between Vega and Gamma as it holds in the European case?
I am aware an exact relation would be difficult to find. But in ...
8
votes
2
answers
4k
views
VIX = Vega of S&P500 options?
ok, so let assume I can predict the daily change in the VIX itself (in points) every day. what would be the best way to play this with OPTIONS? well, obviously VIX options, but if I can look at the ...
- 81
7
votes
1
answer
2k
views
Vol, Gamma, Vega -- essentially all the same?
When talking to traders I hear this sentence a lot
I am a buyer/seller of X
where X = {vol, gamma, vega}
Is X basically all the same -- they are just saying -- I think implied volatility is cheap or ...
7
votes
1
answer
1k
views
Vega in the Heston model
I'm trying to calculate the hedging quantities of the Heston model. I undestand that the replicating portfolio consist of one option, $V = V(S,v,t)$, $\Delta$ stocks and $\phi$ units of the option to ...
- 137
7
votes
1
answer
554
views
Gamma-Vega Neutral Portfolio Not Possible with Only 3 Options
Let's say we have sold a call option, x, on a share and we have 2 other call options, y & z, with different strikes and maturities to try and achieve a portfolio that is both Gamma and Vega ...
- 173
6
votes
1
answer
9k
views
Barrier option (autocallable) Vega profile
I have a question about the Vega profile(graph) on an autocallable option. Generally for a regular option, the vega graph looks like a normal (kinda normal) distribution with the vega highest at-the-...
- 63
6
votes
2
answers
2k
views
Mathematical underpinnings of the square root of time rule
Often when I am reading about options pricing (and/or options greeks) the square root of time continually comes up. What the mathematical justification for why this keeps on turning up?
- 2,562
6
votes
3
answers
744
views
Is Complete Vega Elimination Possible?
I avoid short selling in my strategies. Losing more than invested is not attractive. But at times the implied volatility is too high, I am worried about buying at all and I am trying to filter the ...
6
votes
2
answers
2k
views
how to calculate vega in stochastic vol?
since vega is defined as option value changes regarding the implied vol parallel shift, how is vega defined or calculated in stochastic vol models since implied vol is not an input there? thank you.
- 131
6
votes
3
answers
3k
views
How do we hedge option vega practically?
Suppose I’m a market maker, and I collect some spread buying an option due the flow I get. In this example, I must always quote. I want to hedge as much of the risk as possible over the lifetime of ...
- 196
5
votes
2
answers
656
views
Does higher vega imply higher IV and vice versa
If an option A has higher vega than option B, does that also mean that A has a higher IV than B?
I understand that by definition, a higher vega means that A's price is more sensitive to its IV than B.
...
- 1,404
5
votes
2
answers
2k
views
is there an analytical proof that vega-neutral also provides (gamma & theta) neutral?
I've read an answer here that say if your security has vega, then it has gamma and theta.
is there an analytical proof that vega-neutral also provides (gamma & theta) neutral?
- 77
5
votes
1
answer
322
views
What is vega, really?
Assume for now we are working in a stohastic volatility (SV) setting,
$$
dS_r = \sqrt{v_r} S_r dW
$$
and
$$
dv_r = a(v_r,r)dr + b(v_r,r) dZ
$$
with
$$
dWdZ = \rho dr
$$
Let $C(S_t,v_t,t)$ denote the ...
user34971
5
votes
1
answer
601
views
Can a long put trade be profitable through Vega even if the underlying moves upwards?
Generally speaking, I know when implied vol increases, option prices increase for calls.
However, does the same occur for puts?
If I am expecting implied volatility to increase for an option on an ...
- 2,108
5
votes
1
answer
2k
views
Realizing the same PnL as Gamma Vs Vega
Consider a delta hedged option postion.
Futhermore assume that I can perfectly forecast realized volatility over the life of the option.
Vol I buy the option at = Implied Vol (IV)
Realized volatility ...
5
votes
0
answers
1k
views
Greeks of a Basket Option
I want to estimate delta, vega and gamma for a basket option.
This option is a European Call option.
The underlying is $S=\omega_1 S_1 +\omega_2 S_2$
Where:
$S1$ = stock price of asset 1
$S2$ = ...
- 51
4
votes
2
answers
2k
views
Why do we need to calibrate vega?
I was going through some paid video on options. The tutor in the video asked the following question:
Person $A$ has the following portfolio at the start of April
Portfolio of options with vega $20,...
- 201
4
votes
1
answer
360
views
Vega hedge of a barrier option
I was re-reading Lorenzo Bergomi's paper Smile Dynamics I. On the first page, he makes the point that it is necessary for a model to match the vanilla smile observed in markets in order to incorporate ...
- 747
4
votes
1
answer
1k
views
How can I calculate bucket vega using dupire local volatility surface?
I am trying to calculate the bucket vega of the portfolio which includes mainly vanilla options and some exotic options. I am pricing the value of portfolio with fdm by using dupire local volatility ...
- 41
4
votes
1
answer
223
views
How much does a rise in volatility in a short-term option affect a longer-term option
How would a rise in implied volatility on a short-term option affect the implied volatility of another short-term option with the same strike, but with slightly-longer expiry?
Assuming that the short-...
- 151
4
votes
1
answer
201
views
Is the vega of a portfolio of a long 0.5 delta and short two 0.25 delta calls positive or negative?
More specifically what I am trying to find out is whether the following relationship is always true or not. Same underlying for the calls, assume the most simplistic assumptions (interest rate = ...
- 41
4
votes
1
answer
877
views
Why do options market makers make their spread as wide as the corresponding vega?
I've heard that option market makers make their bid ask spread as wide as the vega of the contract they are quoting. If the quoted spread is narrower than the vega of the option it is said that the ...
- 989
4
votes
1
answer
619
views
Is there a simple, intuitive derivation (using Taylor series) of the following approximation to Vega-weighted Implied Volatility?
The approximation is:
$$\sigma \approx \frac{\sum V_j\sigma_j}{\sum V_j}$$
Background information from the first answer to this post:
"Say that you have a portfolio of options with prices $P_j$. ...
- 41
4
votes
0
answers
248
views
Can the vega of ITM call-options be negative when the distribution of the underlyings returns is negatively skewed?
While calculating european call option prices, using the variance-gamma model formula provided by Madan, Carr & Chang (1998), I noticed that, holding all other things constant, the value of an ITM ...
- 445
4
votes
0
answers
120
views
Spread in Option Quotes
Let's take a look at market-maker's option quote in vol terms: 8.5 / 9.5. In that example bid-ask spread equals 1.0 point of vol.
Can anybody clarifying how market-maker choose amount of spread in ...
- 41
3
votes
2
answers
3k
views
Vega and Gamma signs
Do vega and gamma always have the same sign (ie both positive or both negative)? Under what circumstances can they have opposite signs?
- 2,562
3
votes
1
answer
831
views
Question about the vega of a stock
In Black-Scholes model with constant parameters, a call and a put with the same characteristics have the same vega: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#The_Greeks
Using call-put ...
- 73
3
votes
1
answer
513
views
Calculating Implied ATM Volatility with Vega
Can we calculate Implied ATM volatility with Vega?
Normally, Vega is derived from Volatility, but I wonder the availability of the opposite way.
- 87
3
votes
1
answer
575
views
Simulation of the Vega in Heston model (for Asian Option)
I'm new here and I hope you guys can help me.
I want to calculate/simulate the Vega for my Asian option in the Heston model. The only source I found is the paper of Broadie/Kaya (2004) but they just ...
- 51
3
votes
1
answer
490
views
how to simplify Inflation year-on-year option to Zero-coupon option
Belgrade 2004 paper basically proposes that inflation year-on-year volatilities (and hence yoy options) are basically the spread vols between the Zero-coupon vols from (t0 to T) minus the zero-coupon ...
- 642
3
votes
3
answers
1k
views
Vega in a "constant volatility" Black-Scholes world?
A little confused, I consulted the Wilmott forums for guidance on how I can interpret vega/vomma. Another user's post reminded me that the Black-Scholes model assumes that the underlying has constant ...
- 33
3
votes
0
answers
208
views
Calculate Gamma and Vega of a portfolio of convertible bonds [closed]
I am being asked to calculate the gamma and vega of an existing portfolio of convertible bonds. does anyone has a documentation of direction that i could use to get going pls? This is a premiere for ...
- 171
3
votes
0
answers
220
views
CMS cap has more vega exposure than CMS floor for same strike
When I priced a 10y expiry single look CMS30 ATMF CAP, I noticed that the vega exposure is higher than that of the same 10y expiry single look CMS30 ATMF FLOOR. Why is that?
I have a suspicion that it ...
- 31
3
votes
0
answers
166
views
Spread vol for interest rate spread options in normal environment
Suppose I am long spread option with underlying : rate A - rate B. The vega on the option would be positive. But if I want to compute the option vega with respect to individual rates, can I use the ...
- 45
3
votes
0
answers
265
views
Usages of variance swap
I’m interested in variance swap.
Considered from its feature, variance swap is used for betting the (historical) volatility of underlying asset.
If we use it for hedge tool of Vega or Volga, does it ...
- 31
3
votes
0
answers
1k
views
Derivation of the Pnl of a Delta Hedged Straddle and Risk Reversal
In the link below, in the text it states the following equations:
Delta-hedged straddle P&L = Volatility Risk-premium
×|
Straddle Vega
|
and
Delta-hedged risk-reversal P&L:
...
- 2,562
2
votes
2
answers
2k
views
Relationship between VIX and Vega
Assuming that all other factors (such as underlying price, strike price, etc.) remain unchanged, I want to see how a spike in VIX would affect the price of the average call option? Assume Vega is ...
- 123
2
votes
3
answers
488
views
Purpose of Vega Hedging
I am trying to understand the principle of vega hedging.
When should a market maker vega hedge his position ?
Let's suppose that a market maker delta and gamma hedge himself, and carries his position (...
- 21
2
votes
2
answers
171
views
If you try to capture short term delta by anticipating moves in the underlying, why would vega pnl be so bad?
Since calls and puts have opposite sign delta, but both are positive vega, it feels like a strategy that buys/sell or sells/buys calls and puts on underlying moves to capture delta should generally ...
- 1,347
2
votes
2
answers
3k
views
Vega hedging with implied volatility smile
I have a problem with vega hedging.
Consider the management of an exotic derivative, such as Barrier option. Typically we do the following tasks:
selecting a pricing model, say, a local volatility ...
- 141
2
votes
1
answer
1k
views
Relationship between time decay and gamma
In a paper titled Investing in Volatility published in 1998 by Emanuel Derman, Michael Kamal, Iraj Kani, John McClure, Cyrus Pirasteh, and Joseph Z. Zou, I found the following assertion (on page 9) ...
- 747
2
votes
2
answers
294
views
Calculation Error or High Vega? How to interpret?
I am trying to calculate/interpret Vega. For the example below I get a Vega of ~36.36. I have checked my math multiple times, but would appreciate anyone pointing out any error that I have made. If ...
- 395
2
votes
1
answer
1k
views
European option Vega with respect to expiry and implied volatility
I was told that the Vega of an European option always increases when its time to expiry increases (all else equal). I found this confusing and potentially wrong, but there doesn't seem to be relevant ...
- 115
2
votes
1
answer
89
views
Basel FRTB Vega Sensitivity for Market Risk Capital Standardised Approach
Sorry if this is too simple/obvious a question, but I'm a bit lost looking at the FRTB definition of vega sensitivity for Standardised Approach. Per section 21.25:
...
- 123
2
votes
2
answers
696
views
Binary Option Valuation With Skew
In searching for methods of valuation of Binary options with skew, I have found two formulas which are at odds. I cannot find any other references to this valuation formula. Should Vega be positive ...
- 395
2
votes
1
answer
4k
views
Vega of binary option
I'm calculating the greeks for a hypothetical binary option, and I'm getting a symmetrical parabola for the vega's of both put and call options that are OTM, ATM, and ITM. Both of them dip into ...
- 31
2
votes
2
answers
2k
views
Model calibration volatility surface
Let's say i have an exotic structure that is to be vega hedged dynamically. I choose to price it with a local volatility (which means the model prices in your future vega hedges using all options for ...
- 173