hedging greeks

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CFA_10

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Hi
I have a question regarding greeks hedging.
Delta Gamma hedge: one needs to hedge gamma first(buy/sell option) and thn delta hedge by going long short stock.
But how do we hedge vega or theta as well? What i mean is i want to hedge all greeks. How will i do that??
 
Don’t buy anything.
(To be serious, I’m not sure that there’s an effective way to hedge either vega or theta exposure. There may be some bizarre, triple-anti-volatility ETF out there (though I doubt it), but I’m pretty sure there’s no anti-time derivative.)
 
Makes sense. I think delta gamma hedge may not work perfectly if vol changes drastically.
So can we delta gamma vega hedge? Is it possible to do that?
 
CFA_10 wrote:
kartelite wrote:
CFA_10 wrote:But how do we hedge vega or theta as well?
Click to expand...
Christopher Lloyd and Michael J. Fox might be able to help you on the second one.
For the vega hedge, only this: http://www.sociallunchbox.com/image/pets/everybody-calm-down.
Click to expand...
That wasnt funny.. If you cant help thn just stay the f%&£ out ..
Click to expand...
Besides the fact that the hamster (or whatever it is) picture IS ACTUALLY hilarious, your original post lacks context for anyone to actually answer the question.
You want to hedge theta risk? Sell options. You want to isolate theta risk, build a freaking time machine.
Vega risk? Sell options…the whole point of being long an option is to get positive exposure to increased volatility.
Ask an intelligent question, then maybe you’ll get something better than a dancing chipmunk/hamster/whatever for an answer. Which was, I must say, pretty awesome.
 
kartelite] <p>
CFA_10[/I said:
wrote:
kartelite wrote:
CFA_10 wrote:But how do we hedge vega or theta as well?
Click to expand...
Christopher Lloyd and Michael J. Fox might be able to help you on the second one.
For the vega hedge, only this: http://www.sociallunchbox.com/image/pets/everybody-calm-down.
Click to expand...
That wasnt funny.. If you cant help thn just stay the f%&£ out ..
Click to expand...
Besides the fact that the hamster (or whatever it is) picture IS ACTUALLY hilarious, your original post lacks context for anyone to actually answer the question.
You want to hedge theta risk? Sell options. You want to isolate theta risk, build a freaking time machine.
Vega risk? Sell options…the whole point of being long an option is to get positive exposure to increased volatility.
Ask an intelligent question, then maybe you’ll get something better than a dancing chipmunk/hamster/whatever for an answer. Which was, I must say, pretty awesome.
[/quot
Maybe my question was not so specific.. Fine.. Bt is that reply u give ?
My question was … Is ther a way to hedge delta vega gamma for my portfolio? I want all three to be zero..
Click to expand...
 
CFA_10 wrote:
Maybe my question was not so specific.. Fine.. Bt is that reply u give ? My question was … Is ther a way to hedge delta theta gamma for my portfolio? I want all three to be zero..
Click to expand...
Okay, let me be blunt, because I think your question stems from a misunderstanding of delta-gamma hedging.
The purpose of delta hedging is to LEAVE gamma risk while neutralizing the risk of price changes due to movements in the underlying asset.
Are you comfortable with the following statement: “Options traders typically trade and make plays on gamma, not delta”?
And to answer your question, yes. Although my more detailed reply is probably not the answer you’re looking for.
 
I know traders bet on gamma and not delta..
Let me rephrase my questions using numbers.
I have portfolio with following:
Delta: 550
Vega: 950
Gamma: 2500
Now i can buy any number of options or underlying to make above three zero..
Say there are 2 options available
O1) gamma : 1.5 , vega : 0.3
O2) gamma : 0.1 , vega : 0.9
So, after i solve following two equation
1.5o1 + 0.1 o2 = 2500
0.3 o1 + 0.9 o2 = 950
I will be gamma vega neutral . now i check delta of new portfolio and trade underlying to make it delta neutral aswell.
Is my approach correct? If so, can i add third variable in above equation to solve for theta as well?
 
CFA_10 wrote:I know traders bet on gamma and not delta.. Let me rephrase my questions using numbers. I have portfolio with following: Delta: 550 Vega: 950 Gamma: 2500 Now i can buy any number of options or underlying to make above three zero.. Say there are 2 options available O1) gamma : 1.5 , vega : 0.3 O2) gamma : 0.1 , vega : 0.9 So, after i solve following two equation 1.5o1 + 0.1 o2 = 2500 0.3 o1 + 0.9 o2 = 950 I will be gamma vega neutral . now i check delta of new portfolio and trade underlying to make it delta neutral aswell. Is my approach correct? If so, can i add third variable in above equation to solve for theta as well?
Click to expand...
As a former teaching assistant for Linear Algebra, my first comment would be that yes, you would need a third option (not a linear combination of the other two) to span the three-dimensional vector space.
You can derive some constraints on the third option right now. What will the signs on o1, o2, o3 and the coefficients have to be? Think about if they would all be possible in the financial context here. Can we get something with negative gamma and positive theta?…also, by “buy” do you actually mean “buy/sell”?
 
And you could add a fourth option to include a theta hedge.
However, because delta, gamma, vega, and theta aren’t constant (so the options don’t really form a basis for a vector space), you’ll have to adjust the hedge frequently.
For what it’s worth, I used to teach linear algebra, as well as linear algebra and differential equations. It’s probably not relevant.
 
Yes i meant buy/sell .. And yes we will need one more option to make theta neutral .
I dont have any former education in mathematics.. So will have to work towards understanding of non linear combination of variables.
Thanks cheers
 
CFA_10 wrote:Yes i meant buy/sell .. And yes we will need one more option to make theta neutral . I dont have any former education in mathematics.. So will have to work towards understanding of non linear combination of variables. Thanks cheers
Click to expand...
There’s essentially nothing you can do about the nonlinearity. You buy or sell the appropriate combination of options to create your hedge today, then adjust it tomorrow when the exposures change. You always have a linear approximation to a nonlinear system of equations. (If it were linear, you’d set the hedge and forget it.)
 
S2000magician wrote:
For what it’s worth, I used to teach linear algebra, as well as linear algebra and differential equations. It’s probably not relevant.
Click to expand...
I’d say that options hedging is one of the few concepts in basic finance where linear algebra is actually relevant. Obviously stochastic diffeqs are very relevant on the pricing aspect.
And yeah I’m not an expert in this but I doubt you could get something with opposite signs in theta and vega needed to span. Who knows.
 
kartelite wrote:
S2000magician wrote:For what it’s worth, I used to teach linear algebra, as well as linear algebra and differential equations. It’s probably not relevant.
Click to expand...
I’d say that options hedging is one of the few concepts in basic finance where linear algebra is actually relevant. Obviously stochastic diffeqs are very relevant on the pricing aspect.
And yeah I’m not an expert in this but I doubt you could get something with opposite signs in theta and vega needed to span. Who knows.
Click to expand...
But, as you mentioned above, you can buy and sell. As long as the ratios of vega to theta aren’t the same, Bob’s your uncle. (Of course, if they’re different but extremely close, then the coefficients you calculate might be impractical: buy 17,000,000,000 of option A and sell 17,000,000,100 of option B.)
 
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