Questions tagged [gamma]
The gamma tag has no usage guidance.
62
questions
5
votes
2answers
140 views
Gamma for ATM options with low spots
I'm trying to compute gamma for a vanilla call with spot and strike equal to 0.001.
BLACK & SCHOLES formula gave me a value of 554.761 for gamma which is a very high.
I have then two questions:
...
5
votes
2answers
472 views
Numeric example to understand the effect of option gamma
Gamma of an option is the second partial derivative of the theoretical value of an option wrt the underlying.
It should be the rate of change of Delta wrt to a small change on the underlying.
However ...
2
votes
1answer
50 views
How to prove Gamma is the same for a European call and European put with the same inputs?
I saw from a text "From put-call parity, call and put with the same inputs have the same gamma", but I don't see how put-call parity is related to Gamma. Can someone explain? Thanks!
1
vote
0answers
76 views
Gamma PnL Formula and Break-Even volatility
When we derive the P&L of a delta hedged option we obtain:
$$
\text{P&L}=\dfrac{1}{2}\Gamma(\delta S)^{2}-\theta\delta t
$$
and setting equal to zero and rearranging we obtain:
$$
\dfrac{1}{...
1
vote
1answer
105 views
What does “Gamma profit/loss” mean?
I understand the Greeks as derivatives, but I'm very confused with terms like "Gamma profit/loss""Theta profit/loss". What do these terminologies mean? I've searched online but can't find a proper ...
2
votes
1answer
300 views
Variance of cash gamma (or dollar gamma)
Let us assume we are in the Black-Scholes model. Is there a closed formula for the variance of the cash-gamma? I define cash gamma as $CG = S_t^2 * \Gamma(t,S_t)$, assuming interest rates are 0 to ...
8
votes
2answers
466 views
Expectation of Gamma times S$^2$ in Black-Scholes model
Can somebody prove that:
$$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 $\...
4
votes
2answers
312 views
Conceptual explanation of the relationship between gamma and vega plotted against delta for a European call option
I recently plotted Gamma and Vega against Delta for a European call option and found that the graphs look very similar. This makes sense to me mathematically since the two formulas are pretty much the ...
3
votes
2answers
125 views
Greeks and options hedging
Why is it that theta is sometimes taken as the proxy for gamma of the underlying asset in options hedging?
1
vote
1answer
223 views
Delta hedging/Gamma PnL
Suppose I am long USDIDR straddle with my start of the day delta being USD10m long IDR and USDIDR gamma being $5m.
There is a 1% intra-day IDR strengthening, so my delta becomes roughly long IDR 15m....
1
vote
3answers
118 views
How to compute gamma for at-the-money regular calls and puts when they approach expiration to avoid explosion of portfolio's gamma?
When and at-the-money regular call or put approaches expiration, gamma tends to infinity. However, for practical purposes, there is only a finite change in delta. The problem is that if any of the ...
7
votes
1answer
558 views
Is short-gamma inherently a losing strategy?
With regards to a recent blowup of optionsellers.com - several analysts (specially on Quora) are blaming it on their strategy of being short gamma i.e. selling options. Is it correct to call short-...
0
votes
1answer
345 views
Delta-Gamma VaR question on inputs (do I need only one delta or the delta for the past 500 days?)
When calculating a VaR using the Delta-Gamma approach, I am supposed to use this formula:
∆(V) = Delta * ∆(X) + 0.5 * Gamma * ∆(X)²
where:
∆(V) = change in value of the asset in portfolio
∆(X) = ...
8
votes
1answer
584 views
Swaptions Gamma Interview Questions
A while ago, I interviewed for a trader role and was given the below assignment (I didn't get the job). I wanted to revisit the questions to learn from my mistakes and be better prepared next time. ...
1
vote
0answers
126 views
Can prediction of realized volatility for next day improve delta hedging (gamma scalping)?
Im quite confused. As I understand from standard delta PNL of option + underlying position, pnl is equals to difference between realized and implied vol weighted by gamma.
However, as I understood, ...
0
votes
1answer
424 views
Bucketed gamma for swaptions
For a long 7Y1Y payer swaption, I understand that the overall gamma will be positive.
I see gamma to be positive in 7Y tenor and negative in 8Y - why would that be the case?
Intuitively, how would ...
2
votes
0answers
132 views
Beginner question on Black Scholes
Would you please confirm whether my understanding is correct please? (Sorry a lot of questions...)
1) BS is derived based on the assumption that during an infinitesimal time, we can replicate the ...
6
votes
2answers
5k 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 ...
0
votes
1answer
214 views
If you have a delta-hedged position and you're short gamma, why are spot price movements bad?
I simply can't wrap my head around the concept of Gamma. I've read multiple sites and explanations and for some reason can't wrap my head around the logic, so I feel that it'll really help for me to ...
3
votes
2answers
844 views
Gamma/delta dynamics in the Black Scholes model and it's relation to PnL (Basic of option theory)
If we are in a Black Scholes setup and a I have a Call option and hedged it by shorting delta amount of its underlying.
What does the second derivative of the call with respect to Price of the ...
2
votes
2answers
423 views
Gamma portfolio trading
It is being said that in a long-gamma portfolio, you follow a buy-low sell-high strategy for the underlying stock, which causes you to make profit. The Theta for this portfolio is negative. But it is ...
2
votes
1answer
336 views
construct an option portfolio on a single asset that is both Long Gamma and short vega
everyone, I have come across this question. How can we construct a portfolio that is both Long Gamma and short Vega and how do we actually hedge long Gamma/short vega position?
8
votes
3answers
3k views
What really is Gamma scalping?
How does Gamma scalping really work? It seems there is no true profit scalped. If we look at the simplest scenario, Black-Scholes option price $V(t,S)$ at time $t$ and the underlying stock price at $S$...
2
votes
0answers
46 views
Calculate latest underlying price (or option), given new option (or underlying) market price?
Given a reference underlying price, reference option price, delta and gamma, if I receive a new underlying/option price what equation should I use to calculate the respective option/underlying price (...
4
votes
2answers
3k 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 ...
1
vote
0answers
86 views
gamma-weighted SOIR
I came across a term 'gamma-weighted SOIR' several times recently. it seem like an old term on gamma imbalance. could someone care to explain what this is and the rationale behind it?
1
vote
0answers
1k views
Short Call Hedge. Options and gamma trading
Let’s say a trader sells a Short Call with strike 100 (for making profit with the premium) at-the-money (for highest extrinsic value there). For hedging until expiration, he buys the underlying share ...
7
votes
4answers
6k views
What is the intuitive reason why the Gamma and the Theta tend to have the opposite sign?
Quoting Hull's book:
When gamma is positive, theta tends to be negative. The portfolio
declines in value if there is no change in S, but increases in value
if there is a large positive or ...
6
votes
0answers
1k views
Gamma Imbalance / Exposure
I am currently writing my thesis about the lack of volatility / changing market structure we see nowadays on the financial market. I believe an important factor in this development is the delta-...
2
votes
1answer
304 views
Gamma of a Lookback Option
From this book, http://docs.finance.free.fr/Options/Exotic_Options_Trading.pdf,
it states that
The gamma profile of a Max lookback option becomes intuitive when
viewing it as a ladder option. ...
2
votes
0answers
58 views
What should $T$ be when gamma trading?
I am studying some gamma trading, and there's one thing I don't understand. On the option we are hedging, what should its expiry $T$ be, and for how long should we do the trade?
What I mean is, is it ...
2
votes
1answer
100 views
How does gamma trading depend on $K$?
If we think realized vol > implied vol, then we might go ahead and delta hedge a call, hoping that profits from gamma outweigh the decay.
Question: What should $K$ be on the call? ATM? If so, why? ...
5
votes
1answer
7k views
Proof of gamma profit formula
http://www.volcube.com/resources/options-articles/gamma-hedging-trading-strategies-part-i/
I would like to have proven to me the above formula, mostly because I don't quite understand it. The formula ...
1
vote
0answers
69 views
Stress Test for gamma FX portfolios?
How can I create scenarios to stress gamma FX portfolios? If I shock the underlying for example +/-10%, then I gain in both scenarios. I get to capture some losses if I shock the implied volatility. ...
3
votes
2answers
1k 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?
0
votes
1answer
757 views
Interpretation of an option gamma larger than one
I am working on an option hedging simulation. In this context, I wanted to expand the simulation to include gamma. For testing purposes, I used among others the natural gas futures. When I calculate ...
3
votes
1answer
747 views
How frequently do traders rebalance their gamma hedges?
Say, for instance, that you've set up a delta-neutral straddle (i.e. you are long volatility, short time decay) and want to dynamically hedge your gamma in order to offset losses due to theta. Is ...
6
votes
1answer
6k 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...Mathematically,...
2
votes
1answer
214 views
Using limit orders or stop orders and gamma
From Dynamic Hedging by Taleb:
Risk Management Rule: Option trader lore states that when long gamma, use limit orders. When short gamma, use stop orders.
I cannot understand why this is and the ...
0
votes
1answer
57 views
Known future volatility and difficulty in predicting final P/L
I have started Chapter 1 of Dynamic Hedging by Taleb and it starts by saying
"Even if traders knew the exact future volatility but hedged themselves (rebalanced the gamma) at discretely spaced ...
2
votes
1answer
193 views
Approximation of an option price
The value of an option in the money is 11.50 Euros. The parameters of the market are:
-The price of the underlying stock: 81.4 Euros.
-The volatility ofthe underlying is : 34.65 %
The ...
2
votes
1answer
690 views
Estimating profit/loss of a Gold Futures option using Theta and Gamma
HELP!
I am trying to find how much the underlying price of a gold futures option must move in order to breakeven on owning an option for a day.
I was hoping someone versed in pricing options could ...
3
votes
0answers
89 views
Intraday Value at Risk approximations
We use full valuation of derivatives portfolios using scenarios from historical data.
For simple contracts, this is relatively fast.
For contracts requiring monte carlo simulation, this becomes ...
8
votes
3answers
12k views
How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?
In markets, many instruments are quoted in volatility, but how we can tell what kind of volatility is this? Is it normal volatility, or lognormal volatility. because it affect our hedging positions.
...
5
votes
2answers
881 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?
4
votes
1answer
3k views
Gamma Imbalance Explanation
Can someone please give me an explanation as to what put-call gamma imbalance specifically refers to (imbalance of what?), and why they may exacerbate volatility from a market perspective, and why the ...
2
votes
2answers
3k views
VaR calculation methods of options
I am a little bit confused about VaR in Options and I need a clarification for.
I collected the following formulas, can you suggest what is the best formula and explain me why, please?
0
votes
1answer
117 views
In this scenario could gamma be higher for OTM options?
Let's say there is a $1 stock, with say 1 day to expiration. The 1.5 strike call, is probably a 0 delta at this point; however, a 1 point increase would mean the stock would be at trading at 2 dollars;...
6
votes
3answers
3k views
Greeks: Why does my Monte Carlo give correct delta but incorrect gamma?
For a vanilla European call, my Monte Carlo method gives the right option price and delta but the wrong gamma. In particular, the value of gamma varies wildly each time I run the method. I estimate ...
0
votes
1answer
1k views
Compute cross-gamma
I am trying to use delta-gamma method with montecarlo simulations to calculate the VAR of a portfolio consisting in options and equities.
To use the method I need to compute a gamma matrix, that has ...
